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 - 5.5 Factoring Sums or Differences of Cubes - 5.5 Exercise Set: 30

Answer

$ab(b+10)(b^2-10b+100)$

Work Step by Step

Factoring the $GCF= ab^2 ,$ the given expression, $ ab^5+1000ab^2 ,$ is equivalent to \begin{array}{l} ab^2(b^3+1000) .\end{array} Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $ ab(b^3+1000) ,$ is \begin{array}{l} ab(b+10)[ (b)^2-(b)(10)+(10)^2] \\\\= ab(b+10)(b^2-10b+100) .\end{array}
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