Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 550: 38

Answer

$2x^{2}-x\sqrt[5]{y^{3}}-y\sqrt[5]{y}$

Work Step by Step

Use the FOIL method, along with $\sqrt[n]{a}\times\sqrt[n]{b}=\sqrt[n]{ab},\qquad$ $\sqrt[n]{a^{n}}=(\sqrt[n]{a})^{n}=a$ (for positive a). $F:\quad x\times 2x=2x^{2}$ $O:\quad x\times(\sqrt[5]{y^{3}})=x\sqrt[5]{y^{3}}$ $I:\quad -\sqrt[5]{y^{3}}\times 2x=-2x\sqrt[5]{y^{3}}$ $L:\quad -\sqrt[5]{y^{3}}\times(\sqrt[5]{y^{3}})=-\sqrt[5]{y^{3}\times y^{3}}=-\sqrt[5]{y^{5}\times y}=-\sqrt[5]{y^{5}}\times\sqrt[5]{y}=-y\sqrt[5]{y}$ Add the terms (O and I are like terms...) $...$= $2x^{2}-x\sqrt[5]{y^{3}}-y\sqrt[5]{y}$
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