Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 0 - Section 0.3 - Multiplying and Factoring Algebraic Expressions - Exercises - Page 21: 30


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

Work Step by Step

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