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: 30



Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ (\sqrt[3]{3}-1)(\sqrt[3]{9}+\sqrt[3]{3}+1) ,$ 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} (\sqrt[3]{3}-1)[(\sqrt[3]{3})^2+\sqrt[3]{3}(1)+(1)^2] \\\\= (\sqrt[3]{3})^3-(1)^3 \\\\= 3-1 \\\\= 2 .\end{array}
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