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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.451R (page 561)

In the following exercises, multiply using (a) the Distributive Property (b) the Vertical Method.
$(5 b - 2) (3 b^{2} + b - 9)$ .

Short Answer

Expert verified

(a) Using the distributive property is $(5 b - 2) (3 b^{2} + b - 9) = 15 b^{3} - b^{2} - 47 b + 18$ .

(b) Using the vertical method $(5 b - 2) (3 b^{2} + b - 9) = 15 b^{3} - b^{2} - 47 b + 18$ .

Step by step solution

01

Step 1

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

(a) Use the distributive property to find $(5 b - 2) (3 b^{2} + b - 9)$ .

$\begin{array}{rcl} (5 b - 2) (3 b^{2} + b - 9) & = & 5 b (3 b^{2} + b - 9) + (- 2) (3 b^{2} + b - 9) \\ = & 5 b (3 b^{2}) + 5 b (b) + 5 b (- 9) + (- 2) (3 b^{2}) + (- 2) (b) + (- 2) (- 9) \\ = & 15 b^{3} + 5 b^{2} - 45 b - 6 b^{2} - 2 b + 18 \\ (5 b - 2) (3 b^{2} + b - 9) & = & 15 b^{3} - b^{2} - 47 b + 18 \end{array}$

02

Step 2

Use vertical method.

$3 b^{2} + b - 9 脳 5 b - 2 - 6 b^{2} - 2 b + 18 15 b^{3} + 5 b^{2} - 45 b 15 b^{3} - b^{2} - 47 b + 18$

So, $(5 b - 2) (3 b^{2} + b - 9) = 15 b^{3} - b^{2} - 47 b + 18$ .

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