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