Answer
$x(x+9)^2$
Work Step by Step
Factoring the $GCF=
x
$, the given expression, $
x^3+18x^2+81x
,$ is equivalent to
\begin{array}{l}
x(x^2+18x+81)
.\end{array}
This is a perfect square trinomial since the first and third terms are both perfect squares and the middle term is twice the product of the square roots of the first and third terms. Hence, the factored form is
\begin{array}{l}
x(x+9)^2
.\end{array}