Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.4 - Multiplying Polynomials - Exercise Set: 75

Answer

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

Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$ or the Square of a Binomial, the expression, $ [(xy+4)-6]^2 $, is equivalent to \begin{array}{l} (xy+4)^2+2(xy+4)(-6)+(-6)^2 \\\\= (xy)^2+2(xy)(4)+(4)^2+2(xy+4)(-6)+(-6)^2 \\\\= x^2y^2+8xy+16-12xy-48+36 \\\\= x^2y^2+(8xy-12xy)+(16-48+36) \\\\= x^2y^2-4xy+4 .\end{array}
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