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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 6: Q 201. (page 727)

Multiply a Polynomial by a monomial.
$5 q^{3} (q^{2} - 2 q + 6)$

Short Answer

Expert verified

The required answer is $5 q^{5} - 10 q^{4} + 30 q^{3}$ .

Step by step solution

01

Step 1. Given information

Given expression is $5 q^{3} (q^{2} - 2 q + 6)$ .

02

Step 2. Simplify the expression.

Apply the distributive property.

$5 q^{3} (q^{2} - 2 q + 6) = 5 q^{3} q^{2} + 5 q^{3} (- 2 q) + 5 q^{3} \cdot 6 = 5 q^{5} - 10 q^{4} + 30 q^{3}$

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