Datasets:

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HamAndCheese82

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mathocr-v2

like 2

[ "good" ]

[ "9. $\\displaystyle {x}^{3}-{y}^{3}=(x-y)({x}^{2}+xy+{y}^{2})$" ]

[ "$\\displaystyle =2 \\sqrt{7}\\left\\{(3+\\sqrt{7})^{2}+2+(3-\\sqrt{7})^{2}\\right\\}$" ]

[ "$\\displaystyle =2 \\sqrt{7} \\times 34$" ]

[ "$\\displaystyle =68 \\sqrt{7}$" ]

[ "$\\displaystyle =68 \\sqrt{7}$" ]

[ "good." ]

[ "$\\displaystyle =27-9$" ]

[ "$\\displaystyle =18$" ]

[ "$\\displaystyle x^{3}-y^{3}=(x-y)^{3}+3 x y(x-y)$" ]

[ "$\\displaystyle x-y=5+\\sqrt{7}-(5-\\sqrt{7})=2 \\sqrt{7}$" ]

[ "$\\displaystyle =56 \\sqrt{7}+108 \\sqrt{7}$" ]

[ "20. $\\displaystyle A \\ast B = 9A - 9B$" ]

[ "$\\displaystyle 9\\left(x^{2}+2 x+9y+1\\right)-9(-2 x-y-8)$" ]

[ "$\\displaystyle =9 x^{2}+18 x+81y+9+18 x+9y+72$" ]

[ "$\\displaystyle x+y=1, \\quad x y=-3$" ]

[ "$\\displaystyle x^{2}-x y+y^{2}=(x+y)^{2}-3 x y$" ]

[ "$\\displaystyle x^{2}-x y+y^{2}=(x+y)^{2}-3 x y$" ]

[ "$\\displaystyle =1^{2}-3 \\times(-3)$" ]

[ "$\\displaystyle =1^{2}-3 \\times(-3)$" ]

[ "$\\displaystyle =1+9$" ]

[ "$\\displaystyle \\frac{x^{4}+5 x^{3}+12 x^{2}+20 x+7}{A}$" ]

[ "$\\displaystyle \\frac{x^{4}+5 x^{3}+12 x^{2}+20 x+7}{A}$" ]

[ "$\\displaystyle \\doteq x^{2}+3 x+1 \\quad \\cdots \\quad 3 x+2$" ]

[ "$\\displaystyle \\doteq x^{2}+3 x+1 \\quad \\cdots \\quad 3 x+2$" ]

[ "$\\displaystyle x^{4}+5 x^{3}+12 x^{2}+20 x+7$" ]

[ "$\\displaystyle 16=8-2 x y$" ]

[ "$\\displaystyle 16=8-2 x y$" ]

[ "$\\displaystyle =-4(8-4)$" ]

[ "$\\displaystyle =-4(8-4)$" ]

[ "$\\displaystyle =-16$" ]

[ "$\\displaystyle P(x)=\\left(x^{2}-2 x+1\\right)(x-2)-3 x+6$" ]

[ "$\\displaystyle P(x)=\\left(x^{2}-2 x+1\\right)(x-2)-3 x+6$" ]

[ "$\\displaystyle =x^{3}-2 x^{2}-2 x^{2}-4 x+x-2-3 x+6$" ]

[ "$\\displaystyle x^{3}-4 x^{2}-6 x+4$" ]

[ "$\\displaystyle $" ]

[ "$\\displaystyle $" ]

[ "$\\displaystyle =x^{3}-4 x^{2}+2 x+4$" ]

[ "$\\displaystyle =x^{3}-4 x^{2}+2 x+4$" ]

[ "$\\displaystyle =\\frac{(1+5)(1-5)\\left(1^{2}+5^{2}\\right)\\left(1^{4}+5^{4}\\right)}{4}=\\frac{\\left(1^{2}-5^{2}\\right)\\left(1^{2}+5^{2}\\right)\\left(1^{4}+5^{4}\\right)}{4}=\\frac{\\left(1^{4}-5^{4}\\right)(1^{4}+5^{4})}{4}= \\frac{\\left(1^{8}-5^{8}\\right)}{4}=-\\frac{\\left(5^{8}-1^{8}\\right)}{4}$" ]

[ "Good!\n" ]

[ "perfect!" ]

[ "perfect!" ]

[ "$\\displaystyle 1=x^{3}-y^{3}-12$" ]

[ "$\\displaystyle 1=x^{3}-y^{3}-12$" ]

[ "3)" ]

[ "3)" ]

[ "$\\displaystyle c-a=-(a-b+b-c)=-5$" ]

[ "$\\displaystyle c-a=-(a-b+b-c)=-5$" ]

[ "$\\displaystyle \\frac{1}{2}\\left\\{(a-b)^{2}+(b-c)^{2}+(c-a)^{2}\\right\\}$" ]

[ "$\\displaystyle =\\frac{1}{2}\\left\\{9+4+(-5)^{2}\\right\\}$" ]

[ "$\\displaystyle =19$" ]

[ "$\\displaystyle 19$" ]

[ "$\\displaystyle 19$" ]

[ "Perfect!!" ]

[ "$\\displaystyle x+y=-7, \\quad xy=7$" ]

[ "$\\displaystyle x+y=-7, \\quad xy=7$" ]

[ "$\\displaystyle x^{2}-x y+y^{2}=(x+y)^{2}-3 x y$" ]

[ "$\\displaystyle x^{2}-x y+y^{2}=(x+y)^{2}-3 x y$" ]

[ "$\\displaystyle x^{2}-x y+y^{2}=49-21=28$" ]

[ "$\\displaystyle x^{2}-x y+y^{2}=49-21=28$" ]

[ "$\\displaystyle 28$" ]

[ "Good !" ]

[ "Good !" ]

[ "$\\displaystyle 7 x^{3}-8 x^{2}+7 x-4$" ]

[ "$\\displaystyle 7 x^{3}-8 x^{2}+7 x-4$" ]

[ "$\\displaystyle \\left(x^{2}+y\\right)^{2}(x-y)+x^{2} y-x y^{2}$" ]

[ "$\\displaystyle \\left(x^{2}+y\\right)^{2}(x-y)+x^{2} y-x y^{2}$" ]

[ "$\\displaystyle 8 \\times(-6)$" ]

[ "$\\displaystyle -\\frac{1}{2}(10\\quad =-2(a b+b c+c a))$" ]

[ "$\\displaystyle -\\frac{1}{2}(10\\quad =-2(a b+b c+c a))$" ]

[ "$\\displaystyle -5=a b+b c+c a$" ]

[ "$\\displaystyle a^{4}+b^{4}+c^{4}=\\left(a^{2}+b^{2}+c^{2}\\right)^{2}$" ]

[ "$\\displaystyle =10^{2}$" ]

[ "$\\displaystyle =10^{2}$" ]

[ "$\\displaystyle =100$" ]

[ "$\\displaystyle =100$" ]

[ "$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}+5 b c-10 a b-2 a c\\right)$" ]

[ "$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}+5 b c-10 a b-2 a c\\right)$" ]

[ "$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}-10 a b-5 b c+2 a c\\right)$" ]

[ "$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}+10 a b-5 b c-2 a c\\right)$" ]

[ "$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}+10 a b-5 b c-2 a c\\right)$" ]

[ "$\\displaystyle =16 a^{2}+100 b^{2}+4 c^{2}$" ]

[ "$\\displaystyle =16 a^{2}+100 b^{2}+4 c^{2}$" ]

[ "$\\displaystyle 16 a^{2}+100 b^{2}+4 c^{2}$" ]

[ "$\\displaystyle 5 x+4 x^{2}-2x y+8 y^{2}=-9 x^{2}+6 x y-18 y^{2}$" ]

[ "$\\displaystyle 5 x=-13 x^{2}+8 x y-26 y^{2}$" ]

[ "$\\displaystyle (a+b)^{2}=a^{2}+2 a b+b^{2}$" ]

[ "$\\displaystyle (a+b)^{2}=a^{2}+2 a b+b^{2}$" ]

[ "$\\displaystyle 9 x^{2}+12 x+4$" ]

[ "$\\displaystyle 9 x^{2}+12 x+4$" ]

[ "$\\displaystyle 81 a^{2}-25$" ]

[ "Hi my name is yundo!" ]

[ "Perfect!!" ]

[ "$\\displaystyle 4 b c+12 a c)=216 a^{2}+8 b^{2}-8 c^{2}$" ]

[ "$\\displaystyle 4 b c+12 a c)=216 a^{2}+8 b^{2}-8 c^{2}$" ]

[ "$\\displaystyle -12 a b(6 a+2 b-2 c)$" ]

[ "$\\displaystyle =-72 a^{2} b-24 a b^{2}+24 a b c$" ]

[ "$\\displaystyle =-72 a^{2} b-24 a b^{2}+24 a b c$" ]

[ "$\\displaystyle \\therefore 216 a^{2}+8 b^{2}-8 c^{2}-72 a^{2} b-24 a b^{2}+$" ]