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## Algebra 2

### Course: Algebra 2>Unit 1

Lesson 5: Multiplying binomials by polynomials

# Multiplying binomials by polynomials review

A review of how to multiply binomials like 1 + x by polynomials with more than two terms like x^2 - 5x - 6
We already know how to multiply binomials like left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, minus, 7, right parenthesis. In this article, we review a slightly more complicated skill: multiplying binomials by polynomials with more than two terms.

### Example

Expand and simplify.
left parenthesis, 1, plus, x, right parenthesis, left parenthesis, x, squared, minus, 5, x, minus, 6, right parenthesis
Apply the distributive property.
\begin{aligned}&(\blueD{1+x})(x^2-5x-6)\\ \\ =&\blueD{1}(x^2-5x-6)\blueD{+x}(x^2-5x-6)\\ \end{aligned}
Apply the distributive property again.
equals, start color #11accd, 1, end color #11accd, left parenthesis, x, squared, right parenthesis, plus, start color #11accd, 1, end color #11accd, left parenthesis, minus, 5, x, right parenthesis, plus, start color #11accd, 1, end color #11accd, left parenthesis, minus, 6, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, x, squared, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, minus, 5, x, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, minus, 6, right parenthesis
Notice the pattern. We multiplied each term in the binomial by each term in the trinomial.
Simplify.
\begin{aligned} =&x^2-5x-6+x^3-5x^2-6x\\\\ =&x^3-4x^2-11x-6 \end{aligned}