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: 66

Answer

$x^3+6x^2y+6xy^2+y^3$

Work Step by Step

Using the Distributive Property, the product of the given expression, $ (x+y)(x^2+5xy+y^2) ,$ is \begin{array}{l}\require{cancel} x(x^2)+x(5xy)+x(y^2)+y(x^2)+y(5xy)+y(y^2) \\\\= x^3+5x^2y+xy^2+x^2y+5xy^2+y^3 \\\\= x^3+(5x^2y+x^2y)+(xy^2+5xy^2)+y^3 \\\\= x^3+6x^2y+6xy^2+y^3 .\end{array}
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