Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set - Page 370: 4

Answer

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

Work Step by Step

Divide $4xy$ to each term of the numerator to have: $\require{cancel} \\=\dfrac{4x^3y}{4xy} + \dfrac{12x^2y^2}{4xy}-\dfrac{4xy^3}{4xy} \\=\dfrac{\cancel{4x^3y}x^2}{\cancel{4xy}} + \dfrac{\cancel{12x^2y^2}3xy}{\cancel{4xy}}-\dfrac{\cancel{4xy^3}y^2}{\cancel{4xy}} \\=x^2+3xy-y^2$
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