# Chapter 5 - Section 5.4 - Polynomials in Several Variables - Exercise Set: 51

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

#### Work Step by Step

Using $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the square of the given expression, $(x^2-2y^2)^2 ,$ is \begin{array}{l}\require{cancel} (x^2)^2-2(x^2)(2y^2)+(2y^2)^2 \\\\= x^4-4x^2y^2+4y^4 .\end{array}

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