Answer
$(k-9)^2$
Work Step by Step
Using the factoring of trinomials in the form $x^2+bx+c,$ the given $\text{
expression
}$
\begin{align*}
k^2-18k+81
\end{align*} has $c=
81
$ and $b=
-18
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-9,-9
\right\}.$ Using these two numbers, the factored form of the $\text{
expression
}$ above is
\begin{align*}
&
(k-9)(k-9)
\\&=
(k-9)^2
.\end{align*}