Elementary Algebra

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

Chapter 9 - Roots and Radicals - Chapters 1-9 Cumulative Review Problem Set: 36

Answer

$4(x^{2}+1)(x+1)(x-1)$

Work Step by Step

Upon inspection, we find that $4$ is common to all the terms in the expression. Therefore we factor $4$ from each term of the expression, $4x^{4}-4$ =$4(x^{4}-1)$ Next, we further factor the quadratic equation within the parenthesis: $4(x^{4}-1)$ =$4[(x^{2})^{2}-(1)^{2}]$ =$4(x^{2}+1)(x^{2}-1)$ =$4(x^{2}+1)((x)^{2}-(1)^{2})$ =$4(x^{2}+1)[(x+1)(x-1)]$ =$4(x^{2}+1)(x+1)(x-1)$
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