## Intermediate Algebra (6th Edition)

$(9x+2y)^2$
The two numbers whose product is $ac= 81(4)=324$ and whose sum is $b= 36$ are $\{ 18,18 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $81x^2+36xy+4y^2$, is \begin{array}{l}\require{cancel} 81x^2+18xy+18xy+4y^2 \\\\= (81x^2+18xy)+(18xy+4y^2) \\\\= 9x(9x+2y)+2y(9y+2y) \\\\= (9x+2y)(9y+2y) \\\\= (9x+2y)^2 .\end{array}