Elementary Algebra

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

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.5 - Factoring, Solving Equations, and Problem Solving - Problem Set 6.5: 18

Answer

$4n(n+5)(n-5)$

Work Step by Step

Since $4n$ is common to both the terms of the equation, we take it out as a common factor: $4n^{3}-100n=4n(n^{2}-25)$ We simplify the expression further using the rule $a^{2}-b^{2}=(a+b)(a-b)$: $4n(n^{2}-25)=4n(n^{2}-5^{2})=4n(n+5)(n-5)$
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