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: 29



Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ (2+\sqrt[3]{2})(4-2\sqrt[3]{2}+\sqrt[3]{4}) ,$ use the factoring of 2 cubes. $\bf{\text{Solution Details:}}$ Using the factoring of the sum or difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2)$ the expression above is equivalent to \begin{array}{l}\require{cancel} (2+\sqrt[3]{2})[(2)^2-2(\sqrt[3]{2})+(\sqrt[3]{2})^2] \\\\= (2)^3+(\sqrt[3]{2})^2 \\\\= 8+2 \\\\= 10 .\end{array}
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