Multiplying binomials review

CCSS Math: HSA.APR.A.1
A binomial is a polynomial with two terms. For example, x2x-2 and x6x-6 are both binomials. In this article, we'll review how to multiply these binomials.

Example 1

Expand the expression.
(x2)(x6)(x - 2)(x - 6)
Apply the distributive property.
(x2)(x6)=x(x6)2(x6)\begin{aligned}&(\blueD{x-2})(x-6)\\ \\ =&\blueD{x}(x-6)\blueD{-2}(x-6)\\ \end{aligned}
Apply the distributive property again.
=x(x)+x(6)2(x)2(6)=\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.
=x26x2x+12=x28x+12\begin{aligned} =&x^2-6x-2x+12\\\\ =&x^2-8x+12 \end{aligned}

Example 2

Expand the expression.
(a+1)(5a+6)(-a+1)(5a+6)
Apply the distributive property.
(a+1)(5a+6)=a(5a+6)+1(5a+6)\begin{aligned} &(\purpleD{-a+1})(5a+6)\\\\ =&\purpleD{-a}(5a+6) +\purpleD{1}(5a+6) \end{aligned}
Apply the distributive property again.
=a(5a)a(6)+1(5a)+1(6)=\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:
5a2a+6-5a^2-a+6
Want to learn more about multiplying binomials? Check out this video.

Practice

Problem 1
Simplify.
Express your answer as a quadratic in standard form.
(x+1)(x6)(x + 1)(x - 6)
Want more practice? Check out this intro exercise and this slightly harder exercise.
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