# Multiplying binomials review

CCSS Math: HSA.APR.A.1
A binomial is a polynomial with two terms. For example, $x-2$ and $x-6$ are both binomials. In this article, we'll review how to multiply these binomials.

### Example 1

Expand the expression.
$(x - 2)(x - 6)$
Apply the distributive property.
\begin{aligned}&(\blueD{x-2})(x-6)\\ \\ =&\blueD{x}(x-6)\blueD{-2}(x-6)\\ \end{aligned}
Apply the distributive property again.
$=\blueD{x}(x)+\blueD{x}(-6) \blueD{-2}(x) \blueD{-2}(-6)$
Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.
Simplify.
\begin{aligned} =&x^2-6x-2x+12\\\\ =&x^2-8x+12 \end{aligned}

### Example 2

Expand the expression.
$(-a+1)(5a+6)$
Apply the distributive property.
\begin{aligned} &(\purpleD{-a+1})(5a+6)\\\\ =&\purpleD{-a}(5a+6) +\purpleD{1}(5a+6) \end{aligned}
Apply the distributive property again.
$=\purpleD{-a}(5a)\purpleD{-a}(6)+\purpleD{1}(5a)+\purpleD{1}(6)$
Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.
Simplify:
$-5a^2-a+6$
$(x + 1)(x - 6)$