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: 72

Answer

$2y(3x-5y)(9x^2+15xy+25y^2)$

Work Step by Step

Factoring the $GCF= 2y $, then the given expression, $ 54x^3y-250y^4 $ is equivalent to \begin{array}{l} 2y(27x^3-125y^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, $ 2y(27x^3-125y^3) $ is \begin{array}{l} 2y(3x-5y)[(3x)^2-(3x)(-5y)+(-5y)^2] \\\\= 2y(3x-5y)(9x^2+15xy+25y^2) .\end{array}
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