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: 28

Answer

$8(a+5)(a^2-5a+25)$

Work Step by Step

Factoring the $GCF= 8 ,$ the given expression, $ 8a^3+1000 ,$ is equivalent to \begin{array}{l} 8(a^3+125) .\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, $ 8(a^3+125) ,$ is \begin{array}{l} 8(a+5)[ (a)^2-(a)(5)+(5)^2] \\\\= 8(a+5)(a^2-5a+25) .\end{array}
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