Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2: 60

Answer

The solution set is $\left\{-2, 0, 2\right\}$.

Work Step by Step

Add $-8n$ to both sides to find: $2n^3-8n=0$ Factor out $2n$ to find: $2n(n^2-4)=0 \\2n(n^2-2^2)=0$ RECALL: A difference of two squares can be factored using the formula: $a^2-b^2=(a-b)(a+b)$ Factor the difference of two squares to find: $2n(n-2)(n+2)=0$ Equate each factor to 0 then solve each equation to find: $2n=0 \text{ or } n-2=0 \text{ or } n+2 = 0\\\ n=0 \text{ or } n=2 \text{ or } n=-2$ The solution set is $\left\{-2, 0, 2\right\}$.
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