Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set: 71

Answer

$2a(3a+2b)[9a^2-6ab+4b^2)$

Work Step by Step

Factoring the $GCF= 2a $, then the given expression, $ 54a^4+16ab^3 $ is equivalent to \begin{array}{l} 2a(27a^3+8b^3) .\end{array} Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of $2$ cubes, then the factored form of the expression, $ 2a(27a^3+8b^3) $ is \begin{array}{l} 2a(3a+2b)[(3a)^2-(3a)(2b)+(2b)^2] \\\\= 2a(3a+2b)[9a^2-6ab+4b^2) .\end{array}
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