# Chapter 4 - Polynomials - 4.7 Polynomials in Several Variables - 4.7 Exercise Set - Page 284: 68

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

#### Work Step by Step

Grouping the first 2 terms of each trinomial factor, the given expression, $(x+y+2z)(x+y-2z) ,$ is equivalent to \begin{array}{l}\require{cancel} [(x+y)+2z][(x+y)-2z] .\end{array} Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the expression above simplifies to \begin{array}{l}\require{cancel} (x+y)^2-(2z)^2 \\\\= (x+y)^2-4z^2 .\end{array} Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression above simplifies to \begin{array}{l}\require{cancel} (x)^2+2(x)(y)+(y)^2-4z^2 \\\\= x^2+2xy+y^2-4z^2 .\end{array}

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