Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Exercises: 41

Answer

$x^{2}(x-2)+x(x-2)^{2}=2x(x-2)(x-1)$

Work Step by Step

$x^{2}(x-2)+x(x-2)^{2}$ Evaluate the product in the first term and the power in the second term: $x^{2}(x-2)+x(x-2)^{2}=...$ $...=x^{3}-2x^{2}+x(x^{2}-4x+4)=...$ Evaluate the remaining product and simplify: $...=x^{3}-2x^{2}+x^{3}-4x^{2}+4x=...$ $...=2x^{3}-6x^{2}+4x=...$ Take out common factor $2x$: $...=2x(x^{2}-3x+2)=...$ Finally, factor the expression inside the parentheses to give a more simplified answer: $...=2x(x-2)(x-1)$
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