Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 5 - Section 5.4 - Polynomials in Several Variables - Exercise Set: 68

Answer

$x^3-4x^2y+5xy^2-y^3$

Work Step by Step

Using the Distributive Property, the product of the given expression, $ (x-y)(x^2-4xy+y^2) ,$ is \begin{array}{l}\require{cancel} x(x^2)+x(-4xy)+x(y^2)-y(x^2)-y(-4xy)-y(y^2) \\\\= x^3-4x^2y+xy^2-x^2y+4xy^2-y^3 \\\\= x^3+(-3x^2y-x^2y)+(xy^2+4xy^2)-y^3 \\\\= x^3-4x^2y+5xy^2-y^3 .\end{array}
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