# Chapter 5 - Section 5.4 - Polynomials in Several Variables - Exercise Set - Page 376: 65

$x^3+4x^2y+4xy^2+y^3$

#### Work Step by Step

Using the Distributive Property, the product of the given expression, $(x+y)(x^2+3xy+y^2) ,$ is \begin{array}{l}\require{cancel} x(x^2)+x(3xy)+x(y^2)+y(x^2)+y(3xy)+y(y^2) \\\\= x^3+3x^2y+xy^2+x^2y+3xy^2+y^3 \\\\= x^3+(3x^2y+x^2y)+(xy^2+3xy^2)+y^3 \\\\= x^3+4x^2y+4xy^2+y^3 .\end{array}

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