#### Answer

$2n(n+10)^2$

#### Work Step by Step

Factoring the $GCF=
2n
,$ the given expression, $
2n^3+40n^2+200n
,$ is equivalent to
\begin{array}{l}
2n(n^2+20n+100)
.\end{array}
The trinomial expression above 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}
2n(n+10)^2
.\end{array}