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Algebra basics (ASL)

Course: Algebra basics (ASL) > Unit 7

Lesson 2: Multiplying binomials (ASL)
Math
Algebra basics (ASL)
Quadratics and polynomials (ASL)
Multiplying binomials (ASL)
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Multiplying binomials review

Google Classroom
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.
(x−2)(x−6)=x(x−6)−2(x−6)\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.
=x2−6x−2x+12=x2−8x+12\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.
(−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.
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
Want to learn more about multiplying binomials? Check out this video.

Practice

Problem 1
  • Current
Simplify.
Express your answer as a quadratic in standard form.
left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 6, right parenthesis

Want more practice? Check out this intro exercise and this slightly harder exercise.