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The Distributive Property

By , About.com Guide

What is the Distributive Property in Arithmetic and Algebra?

Named the 'Distributive Property (sometimes referred to as the distributive law) because in essence, you are distributing something as you separate or break it into parts. The distributive property makes numbers easier to work with. In algebra when we use the distributive property, we're expanding (distributing).

The Distributive Property in Arithmetic:


Let's say I have to quickly multiply:

4 x 53
(4 x 50) + (4 x 3)
200 + 12


Let's try another:


One more!

 4 x 27
=4(20 +7)
=4(20) + (7)
=80 + 28


The Distributive Property in ALgebra:

The Distributive Property is handy to help you get rid of parentheses.

a(b + c) = ab + ac

To multiply in algebra, you'll use the distributive law:
= 3x(x) + 3x(4)

You can use the distributive Property to multiply a polynomial by a monomial. You will expand the product of the monomial and polynomial. You can use the distributive property to divide a polynomial by a monomial. Each term is divided by the monomial. You can also use the distributive property to find the product of binomials - as shown:

 (x + y)(x + 2y)
=(x + y)x + (x + y)(2y)
=x2+xy +2xy 2y2
=x2 + 3xy +2y2

Let's try one more:

Here are 8 early algebra worksheets to practice using the distributive property. Answers are included on the 2nd page of the PDF. The first 4 do not include the use of exponents.

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