Answer
$(2x+9)^2$
Work Step by Step
The two numbers whose product is $
4(81)=324
$ and whose sum is $
36
$ are $\{
18,18
\}$. Using these numbers to decompose the middle term of the trinomial results to
\begin{array}{l}
4x^2+36x+81
\\=
4x^2+18x+18x+81
\\=
(4x^2+18x)+(18x+81)
\\=
2x(2x+9)+9(2x+9)
\\=
(2x+9)(2x+9)
\\=
(2x+9)^2
.\end{array}
