nice you should be coming in live and there we are awesome awesome hi everyone this is Chicho welcome to my channel and welcome to another live stream today is october 5th 2020 and we're doing our math tutoring session number 60 let's do some mathematics mainly high school some elementary uh definitely pre-calc is in the game a little bit of calculus a little bit of stats and whatnot and we've done a lot of these in the past and we will be doing a lot more in the future especially considering that right now there's a whole shift happening in education the decentralization of education something's been working towards for a long time now I guess right aside from that welcome this is a math drop in tutoring session uh math discussion open discussion but math discussion supersedes everything else so if there is anything we're talking about that uh is not math related and the math question comes up mathematics takes over okay reset right aside from that let me tell you who I am I am on patreon patreon.com forward slash chicho chy cho if you want to follow this work if you want to support this work if you want to know what this work is about spider-man yo yo how are you doing hello hello and good morning to another set of live streams and if you want to know what this work is about uh patreon is a good place to be okay and I don't point anything behind paywalls everything's creative commons share and share uh like so you can follow work and after a certain period if you think this work is worth supporting supporting this work through patreon is a fantastic way to make sure we continue this project we are live streaming on twitch twitch.tv forward slash chicho live chy cholive if you want to participate in the chat twitch is where you want to be at catholic tradition is how are you doing I still have a few scars from the math session I had with my daughter last night ouch she's definitely not taking to algebra as quickly as my elders said elders yeah everybody's so different catholic tradition this day like uh and parents teaching kids very difficult family members doing the teaching uh is difficult uh there's more challenges involved right lucio petro cian fill the hive of illo ho welcome to our live stream i have no idea how to say your name lory's man how are you doing hello hello and good morning good afternoon to everyone okay and for those of you who are following this work on twitch subscribe to this work on twitch drop in for our tutoring sessions or any of the other live streams we do thank you very much for being here and the mods thank you for taking care of business and for those of you who have been supporting this work through twitch through patreon through other means thank you very much for your support night's of old comics chicho go crazy trying to teach my six-year-old daughter math I get so frustrated when she seems to not try yeah and night's of old comic if they're not trying is because there could be multiple reasons uh pull back on the throttle okay uh you've seen seen my liqueurs I don't think I've seen your liqueurs maybe if you post them on discord I'll see them by the way uh lucio okay but night's of old comic uh pull back on the throttle a little bit if they're not they don't seem to be paying attention and just ease off and just chill with it for a bit and then try to introduce it to them in an indirect kind of way something that they can relate to explain to them as a language if they're not paying attention it could be they're missing a certain concept that is making whatever you're teaching them go over their head so it's they're not grasping the the rhythm of it right it's very tricky it's very personal brother very personal lonely piggy chicho how's life had my first interview with the rc and people has a week went super well in my opinion excited to see the result any snacks for today's mastering I do actually I got the check this out usually I have tahini with honey and maple syrup and stuff like this but this one is sesame seeds sesame sesame seeds with honey so it's not tahini but it's sesame sunflower seeds sorry it's not sesame seeds sunflower seed butter with honey and it's really good it's a different flavor it's very smooth there's no sharpness to it so it's really good as good as a spread and what I do with this as well I'm with peanut butter I take these peanut butter butter and this butter and I mix it in with jam and I use it as a filling for like a flat of cookies that I make sort of a crumble so I make flour layer put a layer down and then I take sesame sunflower seeds or peanut butter and mix it up with jam and then put a layer and then put another layer of flour on top and cook it in a platter so that sort of becomes that sort of becomes my cookie and I got some coffee today to fluffy coffee Catholic traditionist she heard from a few of her friends of the same age at her dance studio that they are not yet having to do algebra oh she's a bit outraged at the time trying this uh Catholic traditionist my students I have the same issue with my students okay when I start teaching them additional content that they need at that time right so I have a lot of students that once we're once we're caught up with class material right they shut down they don't want to learn anything else right so I take the class material and I say well do you know why you're learning this so that's that's one of the things I guess weapons I have at my disposal that to trigger intrigue or interest for my students right when they're learning something in general they have no idea why they're learning it right it may be factoring maybe solving for x may be whatever it might be right they don't know why they're doing it they just go through the motion of doing it so I try to tell them why they're doing it and if they're fairly young and actually any math that they're learning pre grade 11 in my part of world they really don't tell them why they're learning yet it's grade 11 and 12 that you really get into the lies where the supplies right so I start taking whatever it is that they're learning and showing them that it's just part of a bigger puzzle so that's one thing trick I have that I use and then I go do you know why you're learning this for example factoring and they go no and I go okay well this is the reason why you're learning it and I go equal to zero and once you show them that they go oh that's easy and I go do you know what this means and they go no what does it mean I go well it's the x intercepts on a Cartesian coordinate system so all of a sudden I kick them into like two years above what they're learning so start asking them do you know why you're doing this do you know why this works maybe that'll work dov dovda have you ever watched the utopia tv series oh you know what I looked at it I haven't watched it yet Lucio I posted on discord food the pic with lots of bottles was that a while ago or was it just this morning if it was a while ago I see I saw it met a dragon whoa right on time didn't know math discussion is just what we needed today hope you are all doing well are doing awesome so happy to be here awesome to have you nice of all comic I turned into a drill sergeant and next thing I know I'm yelling at my wife I'm nice of all comic funny funny don't turn into a drill sergeant double low negative can we discuss an easy way to simplify radicals maybe how to multiply radicals etc let me write this down and if there's a quick trick for factoring I'm having to resort to a calculator far too often sure so radicals and factoring so let's write this down radicals and factoring okay I'm writing above our my little intro thing my seventh grade needs to needs the why as did I or else is it's a non-star yeah that is a great approach I work on providing a strong sense of how everything Catholic Church says everything she learns can be applied her school is great about doing that awesome awesome olden is what's on the side Kenny Roberts hello hello hello a month ago oh yeah I would have seen it the liqueur picks you posted a month ago there was a yeah I remember people posting some I didn't know it was you some liqueur picks double low negative thanks chichou this online college algebra class is kicking my ass it's like learning math on tape was yeah brutal brutal uh finishing off the intro I do announce these live streams on LO minds vk parlor gab and twitter 30 minutes before we go live and just a few minutes before we go live for unscheduled live streams and you can follow the work there for live streams but we don't have any visuals involved we do record the audio and as podcasts and upload them to soundcloud.com forward slash chichou so you can follow the work there and they should be available on your favorite podcasting platform including Spotify and thanks to Cheryl we just recently got it approved on Apple or iTunes or Apple podcast I don't know what it's called now you used to be called iTunes someone said it's Apple podcast or something now so it should be available on Apple as well and we will be uploading this video this live stream to pitch you to YouTube and if you want to support this work on those platforms you can subscribe you can follow you can like you can turn on notifications participate participate in discussion and if you're on YouTube there should be a join button there where you can join the YouTube channel and support the work that way okay aside from that thank you for being here again I'm just going to take these guys down and let's deal with radicals first okay do you have plans when you will play again with your grandma oh my grandma um I'll let you know I'll let you know my grandma's 92 years old a gang um and she had an episode in the last couple of weeks just because of COVID and she was left alone for a long time and stuff like this just because family couldn't visit and whatnot so um she's going through some hard times and uh I was actually planning to go see her this weekend but unfortunately I didn't get a chance to go see her yeah elder god unfortunately I didn't get a chance to go see her and I hope that I'm going to get a chance to go see her soon okay so I'm on a hair trigger right now um that I might be you know I through three years basically of being on Twitch I've only had to cancel one Twitch livestreams that we've scheduled okay um depending on how things go other I might cancel a few more if we set them or I might try to bring my grandma here and if I bring her here man we're doing like as long as she stays here we'd be doing a math livestream not math the backgammon livestream every day multiple times a day okay so just letting you know just keeping us in the loop my grandmother has lymphoma oh catheter's in my family will keep her in our thoughts and prayers thank you brother family first Cheryl says elder god me too me too let's do this radicals radicals radicals let's take this down let's erase oh no we're not going to erase anything let me put this guy here okay gang let's talk about radicals and who was this that asked about the radicals um double negative double negative was you wasn't it um yeah double negative okay and anybody else by the way if she's okay I'll help what count Miro to a certain degree I'm working on calculus with a student mind that's in college right now so we're working on it together and it's I forgot how fun how amazing calculus is really and we're going through the online course together uh talking about limits right now and simplifying and with functions and graphs and stuff and it is amazing so if calculus questions come up I can I'll try to help uh the intro stuff as we progress together through calculus I can do more and more with you guys I have a pencil ready double negative teach me a great one okay gang if there's any places you don't understand something let me know and we'll go over it okay yeah we're doing and v I saw v subscribe here thank you for the follow or subscribe radicals radicals are the opposite of exponents um powers right but they are powers right so for example the opposite of addition is subtraction the opposite of multiplication is division all three of these are really addition but they're they're unique so we give them their own special symbols right to simplify matters okay who is calling me nvs how are you doing hello everyone hey chico welcome welcome back to another stream okay so opposite of addition is subtraction opposite of multiplication is division right well opposite of powers exponents right so for example in here you could say two to the power of three okay is radicals right is these guys okay but these guys happen to be exponents as well right just like let me erase this okay we know about the factor remind me to do factoring after this right just like this for example right addition and subtraction if you want to subtract something you go something plus negative something that's really subtraction right if you're gonna multiply something you're gonna something times or divide something times one over something that's really division right now radicals is the same thing same type of process happening because if you want to take the radical the root of something what you do is you take the number here and if it's just a square root it goes in the power in the denominator right so if you have a number this is the exponent right two to the power of three and if you go in the exponent divided by something that's the root okay this is what you need to keep in mind okay this is what you need to keep in mind I'm going to do a little bit more of this dingbubber hitchy chow looking forward to some of the these upcoming strength breast selection the alien one should be particularly should be it should be very interesting stuff right now take a look at this thing let's expand on this right so just imagine this what if I said what's the square root and you don't need a two if you say square root right what if I say the square root of five and I ask you to put this in exponent form right well five is to the power of one and the square root means there's a two there so this goes in the denominator in the power so this is really five to the power of a half you're okay with that I'm assuming right if I say what's the cube root of 32 well this guy goes in the exponent in the denominator so this is 32 to the power of one third you're okay with this so far right I hope this is coming out okay by the way again I hope it's not too light okay if I say what's the fourth root of five to the power of eight right hold on five to the power of eight right this guy goes in the exponent in the denominator so this becomes five to the power of eight over four right now this is just a straight up fraction eight over four eight over four reduces down to two so this becomes five to the power of two which is just 25 right so this is one way you can simplify radicals just straight up radicals okay now uh double or negative I don't know what level of radicals we're talking about that you need help with right elder guy I know this mouth well right so this is the basic preliminary stuff that you do to simplify radicals keeping this in mind let's kick this up a notch right let's see let's kick it up notch here one more level so you see the whole thing in one picture and then we'll erase everything we'll go up here and do more and more complicated and build on this okay now keep keep this in mind take a look at this thing what if I told you this what's the cube root of six to the power of seven x to the power of four z to the power of six right and this is the type of stuff you will get if you're starting off with radicals right well to do this there's a couple of ways you can do it right I'm going to do this speedy Gonzales style and then we're going to erase everything and we're going to go through the two different ways you can think about how this works okay one way you can do this is you can say that you're looking for groups of three because you're taking a cube root right chicho if I have one day and two hours played on a specific titan from titan to more kills how many kills that I get per hour I'm not I'm saying sure but I'm going to do the radical right now I should solve this I'll figure it out figure it out then bomb it right so take a look at this thing I'm going to do this quick for you the one method which is really fast and then we'll break it down that you see how it works okay when you're taking the root of something you're really looking for this many groupings right square root means you're looking for a pair cube root means you're looking for triplets fourth root means you're looking for four of a kind right and what that means is if you can find four of a kind inside a radical you can bring it out as a single right so over here six to the power of seven you ask yourself how many times does three go into seven because if you convert this to the root format okay to the exponent format this becomes six to the power of seven over three x to the power of four over three and z to the power of six over two a six over three right now I'm going to erase this I just want you to see what I'm doing right so what you do is ask yourself how many times does three go into seven you say twice so six squared comes out what you have left is what's still inside the radical so three goes into seven twice so six squared comes out and there's one six left over you put a six here how many times does three go into four once so when x comes out and there's one x left over how many times does three go into six twice so sorry z twice so z squared comes out and there's no more z's left over right so this guy simplified is this okay now double or negative let me know if this is okay for you so far and anybody else because I'm going to explain this using two different methods one of them the style that I did now the other one with the roots okay or with the exponent I always feel so embarrassed when it comes to my math skills and the assess I was very bad with math in my school times but this mostly have to do with my teachers I think yeah he was so rude and made sure everyone class knew when I had a bad test result or something probably he thought uh this motivates me but this made me afraid of math and envious you're not alone I almost pulled out of the sciences because of grade 12 math teacher I had he was horrendous okay absolutely horrendous and he he made me dislike math because he was garbage like literally right so keep this in mind okay radical okay now I'm going to break this whole thing down for you so you see it okay a radical has a number here if there is no number it means square root means you're looking for two of a kind right so whatever is in here if you can break it down into groupings of this you can bring it out right double negative yes this is great stuff I'm trying to find the specific problem for you I think what I'm confused on is getting radicals as solutions for equations quadratics and they're like ah okay so what you're having an issue with is linking up the radicals with the factoring because that's really the two connecting together right think bother I did the math I have 4.1 kills a minute nice we call them surds here in the UK surds you call radicals surds no what do you call them iced fixed inside here the grouping you're looking for is this right so if I write down a number let's say this is let's keep it simple leash let's say this is 300 okay and we're looking for the square root and you don't need to put the two there if it's a square root right two what that means is you're looking for pairs in here and pairs you can bring out as singles so what you do is you break down 300 three times 100 100 breaks down to 10 times 10 now you can break that 10 down into his prime factors again right you can break it down into two times five two times five but if we're looking for two of a kind we already found two of a kind two tenths and what you do is a pair can come out of the radical as a single thing so these two guys merge together and come out as 10 on the outside and what you have left on the inside these guys these guys are gone anything that split is gone so this is out this is out so the only thing left inside the square root symbol is a three so it's 10 root three okay strawberry please calculate the curvature of the earth I am so confused why we can never see this supposed curve represented in our real lives because our line of sight is limited right we have mountains we have trees if you if you want if you want to see the curvature of the earth stand at the edge of the ocean where you can see ships coming on the horizon okay grab telescope binoculars and if you know there's a ship coming look at it and what you'll see here's the horizon right and you'll see the mask of the ship slowly coming up as it comes closer and closer to you right that's the curvature of the earth you're looking over a curve so the mask of the ship is rising because it's coming over a curve it's coming over a hill you want to measure it there's different ways of measuring it okay precisely i'm able to get a radical out with the answer but i'm not understanding how to simplify the solution specifically when the answer is a radical as a fraction okay yeah some people have that question all the god right they never thought about it because they read things online they never experiment and experimentation is the key to understanding the world okay you can see the ship reappear if you use a zoom telescope sure but that's because your line of sight is only so far on that same ship start looking at it with the telescope as far as you can and you'll see the same effect because your eyes are at lens you'll see the same effect the ship comes over again right it's just how far you can go one experiment created flatter right so ding bobber uh or not ding bobber double or negative check this out right so you're having a radical without answering the understanding how to simplify the solution specifically when the answer is a radical as a fraction okay so let's erase this right and put different numbers in here let's take this out so let's assume this isn't a square root this is a cube root right a three and in here ha ha c death 420 how are you doing welcome welcome to the live stream crafter low hello let's assume this was 81 over uh 20 no not 20 20 24 24 24 24 okay so we got cube root of 81 over 24 so what you want to do okay break down each one of these individually so take 81 right 81 break it down nine times nine now if we're taking the square root right you already found a pair you could just take the two nines out right but we're looking for the cube root so we're looking for three of a kind so nine becomes three times three nine becomes three times three we're looking for triplets three of a kind so here's a triplet right these three can come out of the radical as a single three and inside is a three left over right so a three comes out so a three comes out you got cube root of three up top cool so if you bring the three in it multiplies itself three times and the times of three it's 81 so this means this right now let's deal with 24 24 24 is two times 12 12 is two times six six is two times three right cool cool we're looking for triplets here's three twos so three twos can come out as a two and there's a three left over inside interesting we've got three over three on the inside keep in mind the 24 was in the denominator here so whatever you do to it has to be in the denominator so the two comes out goes in the denominator here and there's a three left over here cool so this thing so far has simplified to three over two cube root of three over three but three over three is just one anything divided by itself is one so this is three over two cube root of one and the cube root of one is just one so this just simplifies to three over two okay good morning zack the ripper comics ripper how are you doing lack of caring for this how are you doing around i guess elder crafter had math class from 8 p.m 8 a.m to 7 p.m steady for another hour and i'm here to watch for some more nice crafter ripper hope you're doing well now take a look at this thing if this simplified to three over two that means we could have simplified this up here let's see if we can simplify this up here did we do it correctly i think so i hope so let's check it out that's your race days and you always usually want to simplify things well zack says how are you doing well brother thank you very much okay over here 81 what number goes both into 81 and 24 if you know your multiplication you should be able to do this and you should know you should be able to maneuver around numbers from zero all the way to 100 in multiplication pretty well right because you deal with those a lot right if you know how to simplify this you would go so this is one way you could have done it here's another way you could have done it right you could have gone 81 here 81 over 24 oops 24 three goes into 81 27 times three goes into this eight times so this would have been cube root of 27 over 8 and 27 is three times three times three so that's three threes and if you're looking for the cube root three threes can come out as one three if you want we'll break it down this would be cube root 27 breaks down into three times three times three eight breaks down into two times two times two we're looking for the cube root three of a kind so that means these three can come out as a three these twos can come out as a two so it's three over two and there's nothing left inside the radical symbol okay zack finally catching a stream again sleeping schedule doesn't work with the time zone difference of the streams very happy to catch this one awesome remember nice to have you crafter trying to compute multiplication without the rules that you figured out steady is really it's difficult right racer kill how are you doing it's easier to just write it in exponent form and go back after reducing the fraction it is to a certain degree for for some for the more you do the easier it becomes that way but right now in like one of the problems people have in high school mathematics is they're scared of fractions fractions freaks people out which is crazy right one of the reasons fractions freaks people out is because when they're young even an elementary school in math class they tell students just to use a calculator so once you start using a calculator most of them don't even know how to use a calculator property they start using a calculator they don't understand what fractions means they can only understand numbers in decimal format right and then they're lost eagles eagles and cycling how are you doing how did i find your twitch schedule uh how do i find uh love watching you but usually miss you like i do post it on our patreon page and it is on our discord page as well so i do sets unfortunately i don't have set times per week i announce sets as i can fit them in and then i do the streams okay fractions are so simple once you understand the whole yeah it is it is unchartered uncharted days thank you very much for the twitch prime sub appreciative now was it was it double or negative you said you're having a hard time understanding solving four radicals right so let's assume we have the following and let me know if this is along the lines of what you're working on uncharted days jicho you and chatter well doing well thank you very much uncharted days and again thank you for the twitch prime sub now take a look at the same what if i asked you to solve the following uh equation right what if i said three x cubed minus 48 is equal to 100 and uh 100 and i'm trying to think of a number that's gonna have a cube root of it uh and it's going to divide by three so that's 18 18 let's make that let's go 48 48 okay this should work it should give us an answer on following you so far how about multiplying radicals for example for sure we'll do that as well uh since we've got on this let's solve this and then we'll do the multiplication the multiplying radicals is multiplying dividing radicals is easy as well okay but we'll deal with it as soon as we solve this one right so if you want to solve for something solve oops solve it means get the variable by itself to get the variable by itself you undo what's being done to it okay undo what's being done to it so if you know bed mass right if you're simplifying you do bed mass brackets and all that jazz if you're solving you do the opposite of bed mass in the reverse direction so bed mass so this is brackets exponents division multiplication addition subtraction these guys have the same weight right so if you're simplifying you go this way if you're solving you go this way like really now we're solving right so we got to take care of subtraction in addition first so first thing you do is you undo the subtraction that's happening to this so you grab this guy bring it over you go plus 48 okay this becomes 96 right 48 6196 right and over here we got 3x cubed okay then you deal with multiplication and division right random how are you doing okay now you deal with multiplication division so it's three times the x you divide by 3 divide by 3 so on this side we've got x cube is equal to 96 divided by 3 that becomes 32 right 32 9 divided by 3 is 3 6 divided by 2 6 divided by 3 is 2 now don't do it that way if it doesn't go evenly you can just do that because it's obvious right and then you've got to deal with exponents and brackets we've got no brackets what we've got to deal with the exponents first we're going to undo a cube the opposite of cubed is the cube root so you're going to take the cube root of this side and the cube root of this side okay let me erase this so we can do it if you're going to do that then break down 32 32 is four times eight two times two two times four two times four if we're looking for a cube root of something cube root of something we're looking for three of a kind here's three twos three of a kind can come out as a single right so three twos come out as a single two and you got two twos left over and that's here let me write this so we get more space so line up your equal sign you brought three twos out so that's a two and inside the cube root you have two times two left which is four and over here cube root of x cube is just x right that's how you solve that's how the radicals come into play right in terms of multiplying radicals and stuff multiplying dividing let's do one of those guys if you're adding and subtracting radicals they have to be identical if you're multiplying and dividing radicals numbers deal with numbers radicals deal with radicals okay so let's do multiplication and divisions first before we do addition and subtraction because multiplication and division seems to be easier than addition subtraction right so let's just say we have two the square root of five times three the square ten right awesome that makes so much more sense now thanks my pleasure double negative that was really well explained thanks normally i can solve such things but have trouble figuring out how to solve it i'm glad this is helping by the way it's really important radicals are insanely important by the way again right because it's really defines irrational numbers for you right zack chichou have you seen an uptick in your tutoring with the current state of north american education due to the pandemic to a certain degree um it's uh schools are adjusting zack so schools are trying to figure out how to do it so the work i'm getting from schools hasn't kicked up it's actually diminished a little bit from last year but the word of mouth the independent private tutoring that i'm doing and i the school is private as well but they hire me subcontract me the private tutoring the word of mouth is kicked up a little bit especially increasing frequency and the number of people as well right so people that i might might have tutored with like once a week or twice a week previously now we're doing three or four times a week because it's accelerated and there's new people coming in right catholic resistance the following quotient often attributed to galileo has always uh quotation always appeared to me mathematics is the language in which god has written the universe yeah i've read that before catholic to this i like it mass certainly gives us powerful tools to understand the world and indeed so that's just what we had that this they're multiplying each other right if this is the case this is what you do number multiplies number and as long as the radicals are the same radicals this is a square root and that's a square root this multiplies this so two times three is six square root of five times ten is fifty when you multiply this out you should simplify if you can right so break down fifty five times ten five times two square root means you're looking for a pair a pair comes out if there's a number waiting for it on the other side they multiply each other so five times six is 30 what's left in the square root symbol two so it becomes 30 square root of two that's what this times this is okay i hope that's clear now take a look at this what if we had multiple things multiplied together what if we had two square root of three times four square root of six times five square root of uh no let's not make it eight let's make it uh let's make it uh 15 15 do we want that big sure let's make it 15 okay 15 you're good with that right now numbers multiply numbers and then radicals multiply radicals right take a look at this this thing focusing focusing two times four is eight eight times five is 40 right square root of and we can multiply the radicals because all three of them are square root right now in general you're going to multiply them all together and then reduce them right but why do the extra work because you're going to break them apart anyway right so if we do this here let's do this on the side right uh what's the easiest way to do this let's go six times 15 six times 15 oops six times 15 all right six times five is 30 three six times one is six plus nine plus three is nine and then times three so this becomes 270 so you got 270 here right don't do that because the first thing we're going to do whatever we get on the inside we're going to break it apart so if you have things multiply together that's going to give you a big number don't even bother multiplying it because you're going to break it down inside the radical just do this right just write down each one individually or just go whatever the multiplication is i don't care what it is because i'm going to break it down anyway and this thing breaks down into three times six times 15 it's just a shortcut to save you time right lack of caring i also tutor math and it breaks my heart to see bright students think they can't do math because of of they had incompetent lack of caring a 100 percent agree right that's what lights a fire under my ass tell you the truth because once you get a student that flips that all sun goes what it's just you have them it's it's amazing right zach thank you very much for the twitch prime sub right so you tap this thing we don't have to figure out what that is because whatever that was it was just these three multiply together so we just write it down those three multiply together and then we can break these down three times two 15 is three times five right now we're looking for the square root that means we're looking for a pair right if we have multiple pairs we bring them out if we have one pair we bring it up whatever pairs we have we get it and zach says i'm not my student mister he's a kaya how are you doing my math teacher has a uh monotone voice and dead eyes good asmr to go to sleep with right lack of caring exactly exactly lights a fire on their ass so we're looking for a pair because there's a square root here's a pair of threes so pair of threes comes out as a single three multiplies whatever is on the outside three times 40 is 120 because three times four is 12 and you got a zero right so 120 we don't have any other pairs so it's just these guys multiply together two times five is 10 times three is 30 right so all of these multiply together is this now what if all of these were cube root let's assume this was cube root cube root cube root you would do exactly the same but this would just be a cube root and instead of looking for two of a kind you're looking for three of a kind and three of a kind we would have three twos three threes here whoop and three threes would come out multiply the 40 would 120 and on the inside we would just have a two and a five which would be 10 and you'd be doing the cube root of it okay your math teacher must have been a state teacher what's this okay does that make sense okay now take a look at this thing there's other things happen with this right what if we had actually let me rewrite it so you see it what if we had variables multiplied together there were radicals and variables right so let's assume we had two square root of x times three square root of three x right again number multiplies number radical multiplies radical two times three is six square root of x times three x is three x squared and three x squared you can simplify right because x squared is x times x you can grab two x is bring it out as a single so this becomes six x squared of three that's what's left over right so that is six x square over three but what if we had this right this is where the power play comes in right what if this was two x a two square root of x times three cube root of x right Danite how are you doing if you have a square root times a cube root you can't just multiply these together right it doesn't work the numbers work so two times three is six okay you got the six here but you can't go you know you can write it like this square root of x and cube root of x but that's disgustingly messy it's ugly right it's not simple so we're not going to deal with it that way so if you have variables or even numbers that have different radicals in them what you do is you write them as powers now remember we said if it's a square root there's a two here and that goes in the denominator in the power and if we've got a cure root that goes in the denominator in the power right so this really becomes two x to the power of one over two times three x to the power of one over three is that clear double or negative I hope so okay or anyone else watching this by the way right well if that's the case if you have numbers of variables that have the same base and these guys do have the same base if they're multiplying each other then all you got to do is add the exponents right so for example x square times x cube you just add the exponents as x to the power of five yes sir sorry I was passing notes no worries not below negative right so this becomes x to the power of five right if you have two to the power of three times two to the power of eight they have the same base you just add the exponents is two to the power of 11 well that also works for fractions if you have x to the power of a half times x to the power of a third this is adding these guys so that's x to the power of a half plus one over three and that's adding fractions which is finding the common denominator so this becomes x to the power of a half plus one over three how do you add fractions you can do it on the side one over two plus one over three you need a common denominator common denominator six you multiply this by three multiply this by three so that's three plus times two times two two so that's five over six so this becomes six x to the power of five over six and if you're going to write this in radical form it's six the sixth root of x to the power of five does that make sense dovda is your audience mainly children uh not necessarily no we have college university students as well high school kids that's what I really focus on high school mathematics okay but high school mathematics does is not just for kids it's not just for people in high school if you have high school mathematics you can rule the world if you want right if you if you understand fractions and ratios you could be you could go into the stock market and trade to your heart's content as long as you understand what the meaning of the different ratios are that you're looking at right the metrics of any trading system if you consider typical addition always right I hope that's clear we can do another one like this here watch this what if I said they take it to extreme go go radical with it square root of two times cube root of two times fourth root of two cube and let's make this two squared right so we have this all of this multiplying together okay let's do another Zach says nice you can't do an advanced market analysis without some serious foundation statistic statistics it's just it's statistics is is basically looking at the variables right I agree statistics is extremely important you can run filters through and stuff like this but statistics is data data management right what's the z number for normal distribution right the z number it's just a it's just ratios it's just fractions right you take the average subtracted by this divided by standard deviations what's the standard deviation standard deviation is another formula way to number crunch right your data set to get a feel for what the variance is really right so it's just words that sort of terminology that you have to understand what the equations are telling you how you ended up crunching the numbers right sometimes we had these exercises at elementary school that were basic algebra but since they don't teach algebra at elementary school you go to explain it in other in some other way yeah and they should be teaching algebra at your school why aren't they right so if we're going to multiply all these together now if all of these were square roots square root of two times square root of two squared times uh fourth root of two to the power of three oh sorry not fourth root square root of two to the power of three they're all square roots so you just multiply these guys two is two to the power of one you add up the exponent so this is the square root of one three six two to the power of six square root of two to the power of six if you want to think about in a radical form it becomes two six over two which is two cube which is equal to eight right simple enough okay now let's deal with this one where's your coat uh i'd say you need a relatively high level knowledge of statistics to do such jobs that's it a lot of people don't and just plug numbers into formulas agreed very secure uh if you don't if you're just doing trading you don't need that high level of math to be able to invest in a company you need to know what the number is telling you so you don't need to know it's like program it's like using and playing a game you don't need to know the program behind the game you just need to know how to play the game going into the stock market doing trading you don't need to know the program behind the game you need to know how to play the game right and knowing how to play the game is understanding in terms of wall street is understanding what the ratios are telling you right okay square root is the same as one over two blue mama indeed right so take a look at this thing zack chicho i went through my entire us 14 year education preschool k-12 without ever having an algebra class horrible without ever having an algebra this is ripper no way man oh my god insanity insanity right so take a look at this thing let's write all of these as powers right the racer i agree with that you do need at least an elementary level knowledge it's not enough to do it as a job but enough to for personal use yeah and that's what i mean by the way i don't mean going into golden sacks and coming up with new derivative derivatives that you can pedal to uh investors so you can make more money i'm talking about trading right we have algebra in sixth grade here in swiss which is elementary school yeah uh scag math manage education in canada in united states is garbage garbage okay chicho i swear i have a most difficult math class they taught was geometry perhaps it's uh since changed since i graduated in the early 2000s man that's unfortunate lack of care so how is that even possible it's crazy it's crazy so all we do convert these things to exponents right so this becomes two to a power of a half times two to the power of this goes in the denominator two over three times two to the power of three over four well they're the same base so all you got to do is add those guys that's all right so this becomes two to the power of a half plus two over three plus three over four two to the power of common denominators 12 you multiply this by six this becomes six you multiply that by four this becomes eight you multiply that by three this becomes nine so this becomes two to the power of what have you got five six plus eight is 14 14 plus nine is 23 two to the power of 23 over 12 so this is the 12th root of two to the power of 23 now you can simplify this one more level right you can ask yourself you're looking for the 12th root right that means you're looking for 12 of a kind how many 12 of a kinds how many 12s are there in 23 one 12 with 11 left over right there's 23 twos here you can take out 12 sorry 23 twos you can take out 12 of them and there'll be 11 left over right well 12 of them can come out as a single two right because we're looking for the 12th root and you got the 12th root of two to the power of 11 that would be the simplest expression version and that's a 12 of those guys multiply together I hope that's clear I hope that's clear yeah just teach the x yeah I usually when people are trying to learn algebra just solving equations if they're having a hard time I just say placeholder I use a box instead of an x and then I go listen you don't want to use a box all the time it's just crazy just mark it as x marks the spot like a pirate right um what else was there with this and then we were going to go with the factoring right let's talk about factoring let me have a sip of my coffee the phone went away on it my beverage right now is coffee with oat milk it's pretty good I put honey in it lots of honey and I got um sunflower seeds with honey in it it's like uh sunflower butter with honey so it's like peanut butter but sunflower uh butter is very gentle with honey is really good Miro chichu have you heard of the jwe exams if so what's your thought I don't know them oat milk did you say oat milk yeah all their god that will not get a yeah how about a quick and easy factoring lesson chichu I have to go fly plane here soon here soon okay what type of um are we talking about factoring quadratics or just straight up sunflower seeds and honey wow new recipe I learned today it's really good it's a good snack it's better than peanut butter doesn't screw up your omega-3 levels really I'm more of a cashew milk kind of guy looks delicious is that a protein butter um I don't know the other god should know let's do the quadratic okay let's do quadratic I got tea as well by the way why not eat straight protein butter do you think you could do it with pumpkin seeds instead of sunflower seeds you should be able to Miro I haven't tried it though pumpkin seed butter why not I hear that jwe advance is quite difficult yeah I don't know what type of questions they ask for that gang in terms of factoring factoring factoring is you can think about us two different types of things right peanuts are fairly high in protein um now our god says factoring think about it two ways right one of them is you're looking to see what's common between them and you're always going to look for that it's called gcf so the first type of factor you're always going to look for is the greatest common factor it is greatly under used always always I don't care what type of factoring you're trying to do always look for the gcf okay almonds are amazing walnuts for me the best nuts the most nuts that I eat is walnuts and almonds by a long shot like it blows away all the other nuts that I eat all right let's go large gamer friend how are you doing conquer on almonds also yes walnuts yeah so always look for gcf the other types of factoring that you learn straight out are these right difference of squares difference of squares that's what they call them three is simple trinomial trinomial complex trinomial complex trinomial and then you got the quadratic equation quadratic formula x is equal to negative b plus or minus b squared plus uh oops minus minus four ac over two a and then you got long division and synthetic division right synthetic synthetic division where you're breaking uh large polynomials down trying to find out what factors into them right camera why now but when I was super serious on the diet almonds walnuts were the ones I think because of the fats in the brazil nuts lots of not discussion here healthy fats and almonds they're tasty and filling and filling right so we want to do sort of complex trinomial stuff like this but these are all of these guys right check this out all of these guys all of them really what you're doing is you're breaking things down equations or expressions so it's a whole bunch of things multiply together right so you're taking something like this you're taking something an expression like this or an equation like this right that could have have access to different powers and you're gonna try to factor it to get it into things multiplied together to equal zero keep this in mind you're gonna try to convert something like this into things multiplied together to give you zero and the reason you're doing this is because once you convert an equation like this to something like this it means you can use the power of zero where it allows you to take things that are multiplied together to equal zero to split them up to each one equaling zero and we've talked about this right so if you have a times b times c times d equal to zero right how could you multiply four things to give you zero well at least one of them has to be zero at least one of them has to be zero so you set each one equal to zero and you solve for because all all of those would be possible solutions right so you could say a could equal to zero b could equal to zero c could equal to zero and d could equal to zero or a combination of all those right well that's exactly what we do here we say this could equal zero this could equal zero or this could equal zero right and if we took this equation which was different terms added and subtracted together and converted into things multiplied together for example let's assume this was x plus one x minus one two x plus three then you could say x plus one is equal to zero so x is equal to negative one x minus one is equal to zero so x is equal to one two x plus three is equal to zero so x is equal to negative three over two i'm going to do this more clearly by the way i'm just going through a sort of intro speedy gonzala style for you right keep this in mind that is what we're doing and what this means is if this was a function you're finding your x intercepts for a function so if this was a function you're finding your x intercepts that's what you're really doing okay nutrients i love how this translates into great yeah the graphing part of this is the key right but they don't explain this to you they start teaching factoring without putting it into context of what it is right like for me if i was going to teach factoring in grade 10 and i do to students in grade 10 i go through this whole routine i take a nice amount of time like we just did it like in 10 minutes 5 minutes right i take an hour or two hours or a week to explain to a student to appreciate what it is that they're doing and then we kick it back to this now i'm doing a speedy gonzala style because we have a lot of videos online and stuff that we've done regarding this right and if you need to know what they are post you know ask me and discord and i'll link you up to the stuff but let's just go straight up into the factoring okay so you see what the different types of factoring are right now factoring is a simplifying equation a simplifying expressions right you're factoring expressions let's just go straight on into solving right not terrible for you i'm glad gamer friend fiend gamer fiend large a large gamer fiend now take a look at this thing right what if we had this what if i said x squared minus x i'm not going to put the equal sign to yet right let's say i said factor this right factor here let's do it in column format so you see what the difference is right here factor and then we'll put solve here what if i said x squared minus x i said factor this right well you look for a gcf what's the gcf greatest common factor here it's an x they both have an x minimum right this has two x's this has one x so you can take out an x right so when x comes out then you ask yourself what do you multiply x by to give you x squared you multiply by x what do you multiply x by to give you one and a lot of people miss this up right they say oh you took it out so there's nothing there no there is you started with two terms you need two terms okay what do you multiply x by to give you x one so minus one there you just factored this guy right x squared minus x is equal to zero solve this guy right this and this are the same the difference between factoring and solving is factoring is part of solving something a polynomial really right now that we're talking about right it's like simplifying versus solving so in solving in the question itself you'll see an equal sign when they say factor there is no equal sign there you're just trying to factor it right for us to be able to solve this we have to factor it so what we do we factor out an x you get x minus one is equal to zero now we have two things multiplied together to give us zero we've got x and x minus one multiplied together to give us zero so you split them up right you say x could be zero or x minus one could be zero because that's the only way these two things could multiply together give you zero that's not the truth that's not true for any other number I can't say two if this was two right you can't say oh one of these has to be two that doesn't work that way that's the power of zero zero is the only number you could do this with where you could split up the equation right so it has to be zero and I'll show you how you can manipulate it to make sure it's zero right zero well in this case x is equal to zero that's an answer and this becomes x is equal to one because you could just grab this guy bring it over so that's an answer so if x is zero in this then zero this side will be zero which is equal to zero which is true and if x is one then this is true statement right let's do another one what if we had this x squared minus four I would say factor this and over here I would say solve this now double or negative if you're asking about factor and I'm assuming you know that this is a difference of squares if you have any two things subtracted from each other could one of them be a one yeah right there x is equal to one right so if you put one in here you could do a check by the way here let's do a check on this check when you do a check you take the left side of the equation left side and you take the right side right side right the left side is and we're going to check for x is equal to one the right the left side is x squared minus x the right side is zero and our x is one one squared is one minus one is zero so zero equals zero this works this works okay what's typing before that cheeto sorry oh it's okay my channel points are building up I need something oh yeah that's right I'll go have to spend them on and yes I have some ideas oh yeah the channel points I totally forgot about channel points I gotta work on that oh man I totally forgot I gotta do there's something I had in mind to do with sort of got put on a back burner so if you're gonna factor this any two things subtracted from each other you can factor got it any two things subtracted from each other if you got a box mine is a triangle right I don't care what's in the box and what's in the triangle right these are place folders any two things subtracted from each other this is the way you factor them squared of this plus the square root of that times the square root of this minus the square root of that like seriously that's all it's the it's one of the easiest factoring techniques there is okay I missed the previous stream what was in the mysterious small white retro box that you were going to leave to last small white retro box was that the hp calculator bit storm I can't remember small retro box I think so yeah that was the hp calculator you were opening all your things old games and such there was a there was a one special box that was the hp oh it's over there it's in put away it was an hp calculator yeah is that the one elder god I can't remember that had the programmable calculator from 1980s it was 1981 or age two grabbed it that was in a leather case I think that's the one no any two things subtracted from each other you can factor these two are subtracted from each other so square root of x squared square root of box is x plus the square root of four is two square root of x squared is x minus square root of four which is two so we just factored it right solve this well to solve that we have to factor it or one of the ways we could do it is factoring it right so x plus two x minus two now we have two things multiplied together to give us zero we can split them upset each one equal to zero so this x x plus two is equal to zero or x minus two is equal to zero so x is equal to negative two and x is equal to two those are your solutions for this variable was the box uh approximately one foot by one foot if so it was a game console and wires what's that I can't remember so many boxes you can look at it oh he might be talking about the earlier white box the white box we're looking for the white box follow the white rabbit too many prize possessions too many yes in 1980s program calculator yeah that must have been it the hp 1980s program calculator which was really cool actually right now there's other types of factoring we have simple trinomial number three x squared plus uh three x plus two and let's solve this as well x squared plus three x plus two is equal to zero right so this guy is a trinomial trinomial three terms right so if you have a and it's called a simple trinomial because the number in front of the x squared is a one so if you have a number if you have a three term expression and it's a trinomial okay a quadratic really and quadratic is the power on this guy is twice the power on that guy okay and if there's a one in front of the x squared then what you can do is do this let's do trinomials let's do trinomials if this is a simple trinomial then you're looking for two numbers that multiply to give you two and add to give you one now if you know your multiplication table well and you should write what are two numbers that multiply to give you two and add to give you three two numbers that multiply to give you two and add to give you three well two times one gives you two two plus one gives you three so you break this down you go x x because that's x squared and that's an x if this was x to the fourth that would have been x squared and you put x squared here okay then you go two numbers to multiply two add to give you three it's plus two plus one if you multiply this out you're going to get this back should we do a test test on it channel points idea ask chicho at least five thousand to avoid troll abuse at least five thousand to avoid troll abuse so here let's do a test to make sure this is that so test and if they ask you to factor you don't need to test it but let's expand it right let's go x plus two times x plus one this multiplies this this multiplies this this multiplies this this multiplies that x times x is x squared x times one is x two times x is two two times one is two x plus two x i forgot the x is three x so this is x squared plus three x plus two sorry if it's small we're just doing a test so we're just convincing ourselves right so that's the same as that that's just the the pattern that trinomial is going to right so that's factoring that and if you're trying to solve the trinomial you factor it you just got an equal to zero there so this becomes x plus two x plus one you got two things multiplied together to give you zero you can split them upset each one equal to zero x plus two is equal to zero x plus one is equal to zero x is equal to negative two x is equal to negative one right make sense oh ask chichu so like asking math or political questions depending on stream so if someone comes on if they use five thousand points they can ask any question during any stream is that what you're talking about and getting full chichu attention aller god not a bad idea that's a good idea yeah true that's a good idea okay we talk about it if if you guys are game we do we do is that clear double or negative let's do some more of these but we're not gonna factor anymore because factoring comes into play in solving so let's just stick with the solving right because once you learn factoring that really is going to kick you into solving quadratics and when you're solving quadratics what you're doing is finding the x-intercepts I will do that right now right so let's assume we said solve the following equation is equal to zero right and if you want we could do it like this here watch this we could write it out like this x squared minus 7x is equal to negative 10 right so whenever you get something like this got it how about factoring this is a huge number sure double or negatives we'll do it I'm having problems coming up with gcf between these okay we'll do that one next okay I'm just going to write it out here 2x squared 2x squared minus 5x minus 5x plus 3 minus 375 minus 375 what a pain in the ass right but we'll take a look at it right now if you got something like this whenever you're trying to solve for an expression like this or an equation like this you want to if you got multiple different types of x's to a different power right if you have a single x you're just going to get x by itself so move everything else to the other side if you got an x squared and x or x cube and an x squared or whatever it is if you got x's that are two different powers bring everything to one side make the other side equal to zero okay so you can factor one side and utilize the power of zero with the other side being zero tell me about it so we're going to bring this guy over so this becomes x squared minus 7x plus 10 is equal to zero now this is a simple trinomial simple trinomial you're looking for two numbers that multiply to give you 10 add to give you negative seven you can make a table so multiply to give you positive 10 add to give you negative seven two numbers and multiply to give you 10 one times 10 but if you don't add those up that's 11 that doesn't work negative one times negative 10 that multiplies to give you positive 10 but as together to give you negative 11 that's not what we're looking for two times five gives you 10 but two plus five gives you seven right not negative seven so close but no cigar well how about negative two times negative five that multiplies to give you positive seven negative two plus negative five is negative seven which is exactly what we want so you split this up you go x x minus two minus five right and then what you do is you go oh you got two things multiply to give you zero x minus two split them up so x is equal to two and x is equal to five we're done right easy peasy off topic 45 days till the ps5 comes out oh my god that's hype hype hype make sense now let's take a look at this one now this guy is a complex trinomial i'm going to show you there are two ways to solve trinomials quadratics this works when things work out fine we're going to try complex trinomial a technique called the four step method that i've shown before we've covered all this in the language of mathematics playlists there's a ton of videos i put out regarding this by the way okay but let's go over some of these speedy bonzala style right so let's transfer that guy down two x squared minus five x minus three hundred seventy five right and let's set it equal to zero now in general if you can find the gcf to get rid of the number in front of the x square you take it out so for example if you had this two x squared minus 14 x plus 20 you would go hey the gcf of this is two so you can take a two out you're always going to look for the gcf if there's a gcf take it out right you take a two out what do you multiply two to get two x squared x squared what do you multiply two by to give you negative 14 x minus seven x what do you multiply two to give you 20 and 10 and this is what we factored previously so turns into x minus two x minus five easy peasy right so this is a simple trinomial it just had a gcf of two this you can't take the two out not simply anyway you could just go five over two and three hundred seventy five or two but that gives you fractions of complicated things okay so no gcf in terms of just natural numbers or integers right so this is a method that i have to factor these things if it's factorable easily without the quadratic formula take this number and multiply it by this number move it there right and you're dropping it from here so this becomes x squared minus five x three hundred seventy five times two is 750 is it not minus 750 is equal to zero are you okay with that now we're looking for two numbers that multiply to give you negative 750 add together to give you negative five now they have to be if they multiply to give you negative one's positive one's negative if they add to give you negative the bigger number is negative the smaller numbers positive right it is weird i can do this in my head what are two numbers that multiply to give you 750 do you know it i don't know it top of my head i don't know it what are two numbers that multiply to give you together to give you 750 let's do it here multiply together if there is any well there are but they also have to add to give you negative five right for me i will take a calculator and i would go 75 and 10 right so if you go 75 and 10 negative 75 times 10 gives you negative 750 but if you add these guys oh right on bit storm you got right if you add these guys you're going to get negative 80 negative 65 right 65 that doesn't work right that's not negative five right thinking what are two other numbers multiply together to give you negative 750 uh bit storm laid it out for us right but we could also go two times 375 two times negative 375 but those two multiply add it together it doesn't give you negative five that gives you negative 373 so that doesn't work at all and you can go through a whole bunch of process and you're going to find 25 times 30 does it here let's do it 25 times 30 0 5 15 1 6 7 right on right so it's 25 times 30 gives you 750 but we want it to be negative 750 and add it together to give you negative five so it's negative 35 because negative 35 plus 25 is negative five cool we just found the two numbers got it growl hello how are you doing so what you do now is you go okay so this becomes x and x keep in mind this is a quadratic because the power here is double the power on the x here which is one if that was a four that would have been a two and these guys would have been squared if that was a six that would have been a three and these guys would have been cubed right and we've got the numbers positive 25 and negative 30 okay now this guy factored is this guy but we're trying to factor this guy we're trying to factor this guy now what you can do is you're not done with this process you take you take the two that you took here multiply by this you drop it in front of the axis so here you're gonna have two x and here you're gonna have two x and then what you do is let's make sure this is focused and then what you do is you look at each one of these you take out the GCF and dump it is there a GCF between two x and 25 there isn't so you leave this as two x plus 25 is there GCF between two two x and 30 yes there is two so you take the two get rid of it now you got x minus 15 is equal to zero so the answer for this would be two x plus 25 is equal to zero and two x not two x x minus 15 is equal to zero so for this is x is equal to 15 that's one answer here would be two x is equal to negative 25 divided by 2 so x is equal to negative 25 over 2 which is negative 12.5 right does that make sense I understand now basic math is very easy to me it's all them x's that are confusing me right does that make sense I hope so now keep this in mind this is just a I called us the four step method I learned it from a student that learned it from a teacher she had that was like 20 years ago right fan James Bond how are you doing now if if math love it if you couldn't figure out what this combination was you always have your option to go to the quadratic formula so let's use the pretty use the quadratic formula okay I wish I was good at math I usually blank out as soon as an exam is placed in front of me a practice practice large gamer fiend a bit confused though how can you just pull out the two at the start and move it across you it's it's a trick for complex trinomial it's a technique that works there's proofs on it online I've looked through it and they go yep yep it works right but what you're doing is you're taking this multiply by this dropping this you're gerry rigging it really factoring this is a simple trinomial because you can it's a simple trinomial and then you introduce the two back in and then take out the GCF and dump it double negative is that how my issue is coming up with the numbers on your table what multiplies by what to add to another like your four step method though yeah um one way you can do it if the numbers are large you know I'm not a fan of a calculator but when you get large numbers like this use a calculator if you can right just sit there and divide by natural numbers right so take 750 and go divided by 10 and try to get close to a difference of numbers here right so you would go I don't have a calculator here you would go 750 divided by 10 you would get 75 well those can't combine to give you negative five and you go 750 divided by 15 see if that works if that gives you a number an integer see if the difference of those is five if it's not move on and slowly work your way up right and what you're going to find out is at a certain point you're going to cross into numbers the two numbers you're looking for are going to cross each other okay if they exist is there a name for that step I will google it I called it the four step method I don't know what it's called I don't know if there's an official name for it or not bit storm I really don't it works can any robbers laugh out loud you should have divided the x coefficients by two all right the x coefficients well if you divide that you're going to get they're not integers anymore so it becomes even more difficult so for example here let's rewrite this I want to take these guys down gang any questions regarding this fish burn how are you doing hello chichou in chat I think racer kill is saying we should have over here divided everything by two is to get a simple trinomial the problem is we would have had 375 over two now we're looking for two numbers to multiply to give you 375 over two and I have to give you negative five over two which is like oh cool that's what I needed a process for finding them yeah it's really it's a beautiful process it's so simple and usually they teach decomposition in my part of the world and decomposition sucks trying to factor complex trinomials it's sort of the same process but not you take this multiply by this you get this and then you got to split this into two things here I'll show you decomposition it's horrendous just show you decomposite I'll show you decomposition watch this I'm going to erase this and then we'll show you the complex trinomial this is two here two this is the method that they teach in my part they go okay you got a complex trinomial how do you factor this we'll take two times 375 two times negative 375 you get negative 750 okay now what you're thinking about you're thinking about two numbers that multiply together to give you negative 750 apologies for coming in late what's the current topic uh factoring right now we're talking about complex trinomials okay and no worries about dropping in the late so you're going to look for two numbers that multiply to give you negative 750 and they add together to give you negative 5x and we looked at some of these and we got 25 times negative 30 that combination gives you negative 750 so what you do is you split up the negative 5 you go 2x squared and you have to split it up in a way grouping so you group them so you can group the things together right you're going to go 2x squared plus 25x oops x minus 30x minus 375 is equal to zero and then what you're going to do is group these two and those two together okay and if that doesn't work you group the this guy and that guy and that guy and that guy together now these two grouping together and these two grouping together is not going to be the best this and this grouping together and this and this grouping together is the way you want to go with it you know i've forgotten half of this but math is so much fun so much fun right so i'm going to rewrite this and group this and this together so it's going to be 2x squared minus 30x plus 25x minus 375 is equal to zero and then group these two right so if you group these two you just put brackets around them 2x squared minus 30x plus bracket 25x minus 375 is equal to zero now if this was a minus then the sign here would change and you have to keep that in mind as well right and then what you're doing is you're going to take out the gcf now what's the gcf out of here 2x comes out of this right so this becomes x minus 15 okay what's the gcf out of here 25 comes out of this so this becomes plus 25x minus 15 because 25 times 15 is 375 i know that because i got this is equal to zero and then what you do is oh i forgot the x here is 2x that comes out of this right we factor out 2x from this right 2x then what you do is you say oh look there's a gcf here so we grab this and this and bring it up so now you got x minus 15 times 2x plus 25 is equal to zero and that is what we had before but this method is horrendous thank you bitstorm never mind i know i dropped things i make little mistakes here and there i agree with you doing this now is much less daunting than it was during our lessons yeah oh my god what i love about math is at the end of the exercise if it all is right that's so sad that's so satisfying it just works and then this becomes x is equal to 15 and x is equal to negative 25 over 2 which is what we had before right what's the other way to factor this use the quadratic formula right quadratic formula says this let's assume we didn't we didn't want to go through that mental exercise right you go okay this is a quadratic we know it's a quadratic and what we're going to do is just going to use the quadratic formula to factor this negative b plus or minus squared or b squared minus 4ac over 2a and the a b and c in this are the terms here a b and c right it's like this a x squared plus b x plus c right they went over that in class too but they called it factoring by grouping is that what they call it factoring by grouping i don't like factoring by grouping i like the four step method that we did right so what you do is figure out what a b and c are your a is a number here which is 2 your b is a number here and one of the mantras in mathematics the number the sign in front of the number goes with the number the sign in front of the number goes with the number say it again the sign in front of the number goes with the number right the other mantra is reduce before you multiply right so this isn't 5 it's negative 5 and this isn't 375 as negative 375, right? And then all you do you put these where they belong in the quadratic formula, right? So this becomes x is equal to negative b. So negative negative 5 is 5 plus or minus square root of b squared which is going to be negative 5 squared minus 4 times a which is 2 times c which is negative 375 all over 2a which is 2 times 2. So this becomes 5 plus or minus square root of 25. Negative and negative is positive so it becomes plus 4 times 2 is 8 times 375. What's 8 times 375? 8, 44, 56, 66, 24, 30, right? 300 or 3,000? Did we do that correctly? I think so.  I call a system called pi reduction method but I can't say it is the system I teach of. Great to see you're doing math. Yes, talk, x talk programmer. So 40, 0, 4, 56, 0, 6, 24, 30. So 300, 0, 0, all over 4. That means 5 plus or minus square root of 3025 over 4. Now what's the square root of 3025? Yeah, that's good. 3,000 is good. 3,000 is good. Okay. So what's the square root of 3025? Now this I'm going to use a calculator. We already know what it is because if we do the thing but it's 55, right? Chicho from makes my Dave Brighter when he streams releases of it. Something, something, five. Something, something, five. So it's 55. So this becomes 5 plus or minus 55 over 4. That means we got two answers here. x is equal to 5 plus 55 over 4 and x is equal to 5 minus 55, 55 over 4. 55, 5 plus 55 is 60, 60 divided by 4 is 15. 50 divided by 4 is going to be 25, negative 25 over 2, which is the same answer as we got before. So x is equal to 15 and x is equal to negative 25 over 2. Okay, because it was negative 50. This was negative 50 over 4 and 2 goes into both of them, right? Negative 55 over 2 and x is equal to 15. And if you're going to express this in factor format, you would have gone x is equal to 15. Bring the 15 over. So it's x minus 5 and x is equal to negative 25 over 2. Cross multiply 2 up. So 2x is equal to negative 25. Bring the 25 over. So 2x plus 25 is the other factor. Does that make sense? I hope so. Thanks so much for the help, Chicho. You've helped me quite a bit. I have to take off soon. So I'll yield the floor to the other delegates. Awesome. Double 1 negative. I'm glad this helped. And I'm pretty sure it'll help other people that are that need to help with this as well. I can't believe I made a live stream. Ronald Redd, that's what you're doing. I hope you're doing well. We're into the last 15 minutes of this stream. But that was good. We did good mathematics. We did the Speedy-Bonzales cover the fair bit. Just with the factoring stuff, right? Welcome, by the way, Roland. What's our uptime? Uptime. I think we're an hour. Unrecognized. What's going on with my commands? Oh, I gotta do this. What am I doing? Yeah, I want 45 minutes. Good math thing. Good math thing. Or math thing. Can't we just derive the function? We did. You mean take the derivative of the function? Or derive the function? Well, this is the function. This is f of x. This guy. And by the way, gang, what did we just find when we do this? We found the x-intercepts of this quadratic function. So I'm just going to erase this. So I'm going to take these out. So on a graph, this is what we did. Here. We'll leave these guys at the bottom. So on a graph, this is what we ended up doing. x is equal to 15. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. And x is equal to negative 25 over 2 is negative 12.5. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. So here, in the middle. This is a quadratic function that opens up. So we just found this. And the y-intercept is negative 375. Way over here. Negative 375. Zero and negative 375. Not too scale. Not too scale. The graph looks like this. And it's heavier on this side because this is 15 and this is negative 12.5. So the vertex of this is a little bit on this side goes through here and goes like this. We just found this is a horrendous parabola. Not too scale. We just found the x-intercepts of this parabola. That's what we just did. That's what these represent. x is equal to 15 and x is equal to negative 25 over 2. Because if this was a function, we just set y equal to zero. That's what we did. So you can think about it as this is f of x. What happens if y is zero? Zero. What's your x? Your x is this. Because this point here is 15 and zero. And this point here is negative 12.5 and zero. I hope that's clear. I hope that's clear. Should we call the string gang? Okay. Cool, Bon says. You CO. It is Gauss. Roland, I watched so many of these after the fact. Some of the mods are like celebrities. Oh my god. Christian fundamentalist. I hear these names over and over. Nice. Large gamer fiend. What are you doing? And Cheryl of course, right? I'm just out of memory. Flat in the curve. Flat in the curve. Oh no. This is the only time I can happily watch math. Nice. Well, I hope you find more happiness in mathematics in the future. But thank you for the compliment. I did one year econ, but I forgot almost all of it. So sad. But if I do them again, it will come back quick. It will come back quick. And some of the stuff, the important concepts, I'm pretty sure are still in there. I see important stuff that is quite useful, really. Right? Thank you for the questions, gang, by the way. It was good math today. I like going to the speedy Gonzalez format, because we've covered a fair bit of stuff in the past. And for those watching this after the fact, I'll have the links to the playlist in the description of the video, as before always, really, and all the social networks we have are all in the description. You too, Cheryl. You always do the polls for the movie reviews, I think. Yeah. And the comic books. And the comic books. The movies. We're doing movie streams this time around with this set. Have you guys watched all the movies? I've watched two of them so far. I'm going to be watching the other two in the next couple of days. Good memory, Cheryl says. It's Catholic, but your name is kind of right as well. Yeah. So we're going to be doing movie shows. I watched Tombstone and Forbidden Planet. I got El Topo to watch and Breakfast Club to watch as well. Looking forward to El Topo. Oh, my God. Yeah. The useful things are still here, like partial derivatives and the Jacobian Matrix. Who is so cool to do? I'm still throwing up. Oh, my God. Do we know when the movie stream will be? Yeah. I will do everything within my power to make it. Yeah. It's if you go to my Patreon page, it's on the top post right now, the schedule. And if you go to our Discord, it's there as well. Here, I'll give you the link to the Patreon because the Discord, I don't know how to link a specific post in Discord. I don't know why. Or a specific location. I haven't really looked too much for it because there's so much going on. I never it's sort of a rolling thing that goes on. But here's the link to our Patreon page with the schedule. Friday, 8pm. Yeah. And then Monday as well, we pick four new movies. So there's two movie streams we're going to be doing. One of them is reviewing, talking about the movies we picked last time, the four movies and talking about them. And on Monday, I believe, we're going to pick four new movies for the next month to watch. So they're approximately a month apart, these movie streams. Okay. Month, month and a half apart. Gang, aside from that, thank you for being here. Moss, thank you for taking care of business. Gang, thank you for the discussion. Thank you for the recommendations of which nuts are the best proteins and that's the source of Omega, Omega, whatever it is. Okay. New picks Monday at 10am. Monday at 10am. New picks. Cool. Oh, the Cuban cigar catalog. Yeah, I flipped through it, dude. It's just a catalog where we can look at the different cigars and what not. For a decade, I was into cigars in a big way. I worked in an exclusive Cuban cigar store as well for about a year or so. And this is a catalog I picked out. I'll give you guys the lowdown when we do it. Okay. We'll do it in like comic book format, where we're doing the top down view. Just look at the catalog. Okay. It's just lots of pictures and pictures of the cigars. Bye. Much love. Much love gang. Gang, if you want to follow this work, I want Patreon. Patreon.com forward slash chico CHYCHO. If you want to follow this work, if you want to support this work, Patreon is a great way to do so. I don't put anything beyond paywalls. Everything's creative commons. Share and share a like. And for those of you who've been supporting this work through Patreon, thank you very much for your support. It is because of you that we're able to continue this work. Okay. We are live streaming on Twitch, twitch.tv forward slash chico live CHYCHO L I V E. If you want to participate in the chat, Twitch is where you want to be at. And for those of you who've been subscribing, following through Twitch, thank you very much for the subscribe, for the follows, for the discussions, for being here. It is in large part because of you as well, that we're able to do this work.  And for unscheduled live streams, we do announce a few minutes before we go live and we do share some additional content there as well. There are podcast audio of live streams when we just do open discussions, when there's no visuals involved. And those are available on soundcloud.com forward slash chico. And they should be available on your favorite podcasting platform, including spot spotify and iTunes or Apple podcast. Now, thanks to Cheryl for setting that up. And this video will be uploaded to BitShoot and YouTube. And you can support this work by on those platforms, by subscribing, by following, by turning on notifications and commenting and sharing. And if you're on YouTube, you can support this work by joining YouTube membership. And thank you very much for joining YouTube membership and for the support. Thanks for the stream. From my pleasure, I bring that great name. Domino said has to be in Cuban screen. Domino said, Oh man, I got to get my Domino set up. I'll try to find it. I'll try to find it. Just found your Parler. Nice. Nice picture. These are awesome. A large camera fiend. But yeah, thanks for today's stream. I came a little bit late, but never mind. Next time we'll be here early. Awesome. Awesome. And just follow the Patreon feed.  You can just follow. And after a while, if you do think that this work is worth supporting, supporting it through Patreon is a great way to do so. But I do announce the schedule on there. Okay. If you want to get it. Cigar ASMR is the best one. No contest. And at some point, I'm going to get back into smoking cigars. We'll see. Gang, I hope you have a fantastic day and I'll see you guys in tomorrow's stream. We've got six more coming this week. Bye everyone.


In today's session, we are going to discuss the concept of yield curves. When we discuss the concept of stock markets, financial structure, financial system, it is important to understand what is meant by a yield curve. The yield curve basically explains the relationship between yields and the various maturity times. In other words, we can say that it is a linear relationship between the maturity of bonds or stocks or whatever financial instrument you are taking. And it is on one hand and on the other side, we are going to take into account the interest rate or the yields which we are going to get from these stocks or bonds or any other financial instruments. So this is a line in which we take the yield or interest rate on the vertical axis and on the x axis or on the horizontal axis, we take the maturity time period. The slope of the yield curve tells us how our economic situation is going to be in the future. So it predicts that what is going to happen in the financial markets and overall economy in the coming time or in future. So we have three types of yield curves. The first one is the normal yield curve which is an upward sloping. I am going to draw it for you in a while. So upward sloping yield curve, we have an inverted downward sloping yield curve and the third type of yield curves we have is a flat yield curve. So according to the maturity time period of returns, the shape of the yield curve is going to be defined or it tells us how the financial sector is going to influence the economy in the future and how the economy is going to perform over a period of time. So when we talk about the normal or an upward sloping yield curve, it means that longer term bonds or the bonds whose maturity time period is more, their yield is obviously more. So in the diagrammatic form, if we plot the yield curve and upward sloping yield curve, we can take the yield or the interest rate on the vertical axis and the maturity time of bonds on the horizontal axis. So it shows that if a bond is going to mature in for example one year, the interest rate it is going to yield is for example 4%. But if we are talking about a bond which will mature in say 10 years, naturally the yield or the interest rate which we are going to get from this particular bond which is going to mature in 10 years will be 12%. So if the maturity time period is longer, we are going to have a higher interest rate. As a consequence, we get this upward sloping yield curve. So if this is a situation, then we say that people are happy about the, they are optimistic about the future and they know that if we invest for the long term, then naturally we are going to benefit a lot. And that is why it is promised that the interest rate on the bonds in the future time period will be higher as compared to the short term bonds that you are getting for the return. So this is the normal usual shape of a yield curve. And if this is a situation, it shows that there is prosperity coming in the future or things are good, the economy is expanding, it is improving. On the contrary, if we see that the long term maturity bonds of the future have less interest rates and the short term bonds have higher interest rates, then we come across a different kind of a situation which can be explained in terms of an inverted yield curve. So as the name specifies, it has been inverted here, which we just talked about. What was it before and what should usually be? When you invest in long term bonds, the interest rate that you get on the long term bonds is promised. That is higher as compared to when you buy short term bonds that are going to be stolen after a year or a year and a half or two years, the interest rate should naturally be less. But sometimes when investors are forcing that things in the future are not going to be okay, they are going to be some recession or some pessimist opinion of the investor, so they are seeing that in the future it is possible that we do not promise a higher interest rate. We are borrowing investment bonds for the long term. We are selling bonds to people in the form of bonds for the long term which will be mature over 5 years or 6 years or 10 years. The interest rate on that is offering a little. In the future, things are not going to be better. Rather, they give promise a higher interest rate on short term bonds. If such a situation happens, this kind of a situation can be explained graphically using the concept of inverted yield curve. And if we are forcing, if your yields are inverted by accounting for long term or short term, that means that something is going to be wrong in the future. People are not happy that your investors are not forcing that there will be a good situation. So, when we talk about the inverted yield curve, again, I would take the yield or the interest rate on the vertical axis. And the maturity time period, different bonds are taking time period when they will be mature. Again, it will be 1 year, 2 years, 3 years, something like that. So, the inverted yield curve will be something like this in which you can see that the short term bonds are higher and the long term bonds are lower. So, suppose this is 2% and this is 4%. So, you can see that if such a situation happens, we explain this particular situation or scenario through the inverted yield curve. The third type of yield curve we have is the flat yield curve. So, what is the flat yield curve? If you are sitting in a situation of a normal yield curve and things are not okay in the future, it is forcing that there should be no higher interest rate on the long term stocks or long term bonds. So, in such a situation, the curvature of the curve becomes like a straight line. So, similarly, if things are getting better, there is no recession or financial or economic situation of the economy. But it is forcing that things will get better in the future. So, what will happen is that the long term bonds will start increasing the interest rate. So, when it starts increasing naturally, the downward sloping inverted yield curve will change in its curvature and it will start becoming flat. So, when it becomes flat, we would say that this is a special type of another special type of yield curve which is a flat yield curve. Or again, we observe that whenever there is an economy which is transitioning or moving from a recession situation, an economic scenario where there is recession to some sort of recovery, then you will see that the inverted yield curve will start becoming flat and that particular situation will be represented through the flat yield curve. And eventually, there may be a situation where things go better, things improve significantly, the situation has become much better due to the financial market. And again, the same situation has happened. Contrary to the past, you are being offered a higher interest rate on the long term bonds. On the short term bonds, you are being offered a lower interest rate. So, in such a situation, your inverted yield curve will transform into a normal yield curve. But the phase in between that will be represented through a flat yield curve. And what does a flat yield curve mean? That you can represent it through a horizontal straight line.