# Chapter 8 - Polynomials and Factoring - Chapter Test - Page 527: 27

The Distributive Property states that for three variables $a, b,$and $c$, $a*(b+c) = ab+ac$. When there are two binomials, then the first value of the first binomial is multiplied by the values of the second binomial. Then, the second value of the first binomial is multiplied by the values of the second binomial. Then, like terms are combined.

#### Work Step by Step

Example: $(x+a)(x+b)$ $x*x+x*b+(a*(x+b))$ $x*x+x*b+a*x+a*b$ $x^2+bx+ax+ab$ $x^2+ax+bx+ab$ $(x+1)(x-4)$ $x*x+x*(-4)+(1*(x-4))$ $x*x-4*x+1*x+1*(-4)$ $x^2-4x+x-4$ $x^2-3x-4$

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