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

(x + 2) (x - 7)

. In this article, we review a slightly more complicated skill: multiplying binomials by polynomials with more than two terms.

Expand and simplify.

(1 + x) (x^{2} - 5 x - 6)

Apply the distributive property.

\begin{aligned} (1 + x) (x^{2} - 5 x - 6) \\ = & 1 (x^{2} - 5 x - 6) + x (x^{2} - 5 x - 6) \end{aligned}

Apply the distributive property again.

= 1 (x^{2}) + 1 (- 5 x) + 1 (- 6) + x (x^{2}) + x (- 5 x) + x (- 6)

Notice the pattern. We multiplied each term in the binomial by each term in the trinomial.

Simplify.

\begin{aligned} = & x^{2} - 5 x - 6 + x^{3} - 5 x^{2} - 6 x \\ = & x^{3} - 4 x^{2} - 11 x - 6 \end{aligned}

Want to learn more about multiplying binomials and polynomials? Check out this video.

Practice

Expand and simplify.

(c^{2} - 6) (2 c^{2} + 3 c - 1)

Want more practice? Check out this exercise.

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