Answer
$(9x+2y)^2$
Work Step by Step
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}
