Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set: 71

Answer

$(\sqrt[3]{x}+1)(\sqrt[3]{x}-4\sqrt{x}+7)=\sqrt[3]{x^{2}}-4\sqrt[6]{x^{5}}+8\sqrt[3]{x}-4\sqrt{x}+7$

Work Step by Step

$(\sqrt[3]{x}+1)(\sqrt[3]{x}-4\sqrt{x}+7)$ Evaluate the product: $\sqrt[3]{x^{2}}-4\sqrt[3]{x}\sqrt{x}+7\sqrt[3]{x}+\sqrt[3]{x}-4\sqrt{x}+7=...$ Simplify: $...=\sqrt[3]{x^{2}}-4(x^{1/3})(x^{1/2})+8\sqrt[3]{x}-4\sqrt{x}+7=...$ $...=\sqrt[3]{x^{2}}-4x^{5/6}+8\sqrt[3]{x}-4\sqrt{x}+7=...$ $...=\sqrt[3]{x^{2}}-4\sqrt[6]{x^{5}}+8\sqrt[3]{x}-4\sqrt{x}+7$
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