Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.5 - Multiplying and Dividing Radical Expressions - 7.5 Exercises - Page 475: 36



Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ (\sqrt[3]{9z}-2)(5\sqrt[3]{9z}+7) ,$ use the FOIL method and then combine like terms. $\bf{\text{Solution Details:}}$ Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{9z}(5\sqrt[3]{9z})+\sqrt[3]{9z}(7)-2(5\sqrt[3]{9z})-2(7) \\\\= 1(5)(\sqrt[3]{9z})^2+7\sqrt[3]{9z}-2(5)\sqrt[3]{9z}-14 \\\\= 5(\sqrt[3]{9z})^2+7\sqrt[3]{9z}-10\sqrt[3]{9z}-14 \\\\= 5\sqrt[3]{(9z)^2}+7\sqrt[3]{9z}-10\sqrt[3]{9z}-14 \\\\= 5\sqrt[3]{81z^2}+7\sqrt[3]{9z}-10\sqrt[3]{9z}-14 .\end{array} By combining like terms, the expression above is equivalent to \begin{array}{l}\require{cancel} 5\sqrt[3]{81z^2}+(7-10)\sqrt[3]{9z}-14 \\\\= 5\sqrt[3]{81z^2}-3\sqrt[3]{9z}-14 .\end{array}
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