Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 51



Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the FOIL method, and the properties of radicals, the given expression, $ (\sqrt{x}+5)(\sqrt{x}-3) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{x}(\sqrt{x})+\sqrt{x}(-3)+5(\sqrt{x})+5(-3) \\\\= x-3\sqrt{x}+5\sqrt{x}-15 \\\\= x+2\sqrt{x}-15 .\end{array} Note that all variables represent positive real numbers.
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