# Chapter 5 - Section 5.4 - Polynomials in Several Variables - Exercise Set - Page 376: 71

$x^6y+x^4+2x^2+x^4y+1$

#### Work Step by Step

Using the Distributive Property, the product of the given expression, $(x^2+1)(x^4y+x^2+1) ,$ is \begin{array}{l}\require{cancel} x^2(x^4y)+x^2(x^2)+x^2(1)+1(x^4y)+1(x^2)+1(1) \\\\= x^6y+x^4+x^2+x^4y+x^2+1 \\\\= x^6y+x^4+(x^2+x^2)+x^4y+1 \\\\= x^6y+x^4+2x^2+x^4y+1 .\end{array}

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