Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.7 Polynomials in Several Variables - 4.7 Exercise Set: 65

Answer

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

Work Step by Step

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