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: 37



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). $F:\quad x\times 2x=2x^{2}$ $O:\quad x\times(-\sqrt[3]{y^{2}})=-x\sqrt[3]{y^{2}}$ $I:\quad \sqrt[3]{y^{2}}\times 2x=2x\sqrt[3]{y^{2}}$ $L:\quad \sqrt[3]{y^{2}}\times(-\sqrt[3]{y^{2}})=-\sqrt[3]{y^{3}\times y}=-\sqrt[3]{y^{3}}\times\sqrt[3]{y}=-y\sqrt[3]{y}$ Add the terms (O and I are like terms...) $...$= $2x^{2}+x\sqrt[3]{y^{2}}-y\sqrt[3]{y}$
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