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 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 687: 99

Answer

$(x+10)(x-10)$

Work Step by Step

The expressions $ x^2 $ and $ 100 $ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $ x^2-100 ,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (x)^2-(10)^2 \\\\= (x+10)(x-10) .\end{array}
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