## Intermediate Algebra (12th Edition)

$(x+y+3)^2$
$\bf{\text{Solution Outline:}}$ To factor the given expression, $(x+y)^2+6(x+y)+9 ,$ simplify the expression using substitution. The resulting expression is a perfect square trinomial. Use the factoring of perfect square trinomials. Finally, substitute back the original expression. $\bf{\text{Solution Details:}}$ Let $z= (x+y) .$ The given expression becomes \begin{array}{l}\require{cancel} z^2+6z+9 .\end{array} The trinomial above is a perfect square trinomial. Using $a^2\pm2ab+b^2=(a\pm b)^2,$ the expression above is equivalent to \begin{array}{l}\require{cancel} (z+3)^2 .\end{array} Since $z= (x+y) ,$, then the expression above becomes \begin{array}{l}\require{cancel} ((x+y)+3)^2 \\\\ (x+y+3)^2 .\end{array}