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 4 - Polynomials - 4.6 Special Products - 4.6 Exercise Set: 84

Answer

$x^3-125$

Work Step by Step

Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $ (x-5)(x^2+5x+25) $, is equivalent to \begin{array}{l}\require{cancel} x(x^2)+x(5x)+x(25)-5(x^2)-5(5x)-5(25) \\\\= x^3+5x^2+25x-5x^2-25x-125 \\\\= x^3+(5x^2-5x^2)+(25x-25x)-125 \\\\= x^3+0x^2+0x-125 \\\\= x^3-125 .\end{array}
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