# Chapter 5 - Section 5.4 - Multiplying Polynomials - Exercise Set - Page 289: 43

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

#### Work Step by Step

Using the square of a binomial, $(a+b)^2=a^2+2(a)(b)+b^2$, the given expression is equivalent to \begin{align*} & [(xy+4)-6]^2 \\\\&= (xy+4)^2+2(xy+4)(-6)+(-6)^2 \\\\&= (xy+4)^2-12(xy+4)+36 \\\\&= (xy)^2+2(xy)(4)+(4)^2-12(xy+4)+36 \\\\&= x^2y^2+8xy+16-12xy-48+36 \\\\&= x^2y^2+(8xy-12xy)+(16-48+36) \\\\&= x^2y^2-4xy+4 .\end{align*}

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