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## Algebra basics (ASL)

### Course: Algebra basics (ASL)>Unit 7

Lesson 2: Multiplying binomials (ASL)

# Multiplying binomials review

A binomial is a polynomial with two terms. For example, x, minus, 2 and x, minus, 6 are both binomials. In this article, we'll review how to multiply these binomials.

### Example 1

Expand the expression.
left parenthesis, x, minus, 2, right parenthesis, left parenthesis, x, minus, 6, right parenthesis
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.
equals, start color #11accd, x, end color #11accd, left parenthesis, x, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, minus, 6, right parenthesis, start color #11accd, minus, 2, end color #11accd, left parenthesis, x, right parenthesis, start color #11accd, minus, 2, end color #11accd, left parenthesis, minus, 6, right parenthesis
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.
left parenthesis, minus, a, plus, 1, right parenthesis, left parenthesis, 5, a, plus, 6, right parenthesis
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.
equals, start color #7854ab, minus, a, end color #7854ab, left parenthesis, 5, a, right parenthesis, start color #7854ab, minus, a, end color #7854ab, left parenthesis, 6, right parenthesis, plus, start color #7854ab, 1, end color #7854ab, left parenthesis, 5, a, right parenthesis, plus, start color #7854ab, 1, end color #7854ab, left parenthesis, 6, right parenthesis
Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.
Simplify:
minus, 5, a, squared, minus, a, plus, 6

Problem 1
• Current
Simplify.