Multiplying monomials by polynomials review

We use the distributive property to multiply monomials by polynomials. For example, 2x(3x+7) = 6x^2+14x. This article provides a brief review of the topic and gives you a couple of practice problems to try on your own.

In order to multiply monomials like

6 z^{2}

by polynomials like

7 z^{2} + 3 z - 2

, we need to apply the distributive property.

Example

Simplify.
Express your answer as a trinomial.

6 z^{2} (7 z^{2} + 3 z - 2)

This is a distributive property problem. How can we distribute

6 z^{2}

to each term inside of the parentheses?

This product is equal to

42 z^{4} + 18 z^{3} - 12 z^{2}

Want to learn more about multiplying monomials by polynomials? Check out this video.

Practice

Problem 1

Simplify.
Express your answer as a trinomial.

- n^{2} (n^{2} + 5 n + 6)

Want more practice? Check out this exercise.

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