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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.452R (page 561)

In the following exercises, multiply. Use either method.
$(m + 6) (m^{2} - 7 m - 30)$ .

Short Answer

Expert verified

The solution is $(m + 6) (m^{2} - 7 m - 30) = m^{3} - m^{2} - 72 m - 180$ .

Step by step solution

01

Step 1

Recall the distributive property that $a 路 (b + c) = a 路 b + a 路 c$ .

Use the distributive property to perform the multiplication operation.

$\begin{array}{rcl} (m + 6) (m^{2} - 7 m - 30) & = & m (m^{2} - 7 m - 30) + 6 (m^{2} - 7 m - 30) \\ = & m (m^{2}) + m (- 7 m) + m (- 30) + 6 (m^{2}) + 6 (- 7 m) + 6 (- 30) \\ = & m^{3} - 7 m^{2} - 30 m + 6 m^{2} - 42 m - 180 \\ (m + 6) (m^{2} - 7 m - 30) & = & m^{3} - m^{2} - 72 m - 180 \end{array}$

So, $(m + 6) (m^{2} - 7 m - 30) = m^{3} - m^{2} - 72 m - 180$ .

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