Answer
$ab(b+10)(b^2-10b+100)$
Work Step by Step
Factoring the $GCF=
ab^2
,$ the given expression, $
ab^5+1000ab^2
,$ is equivalent to
\begin{array}{l}
ab^2(b^3+1000)
.\end{array}
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $
ab(b^3+1000)
,$ is
\begin{array}{l}
ab(b+10)[ (b)^2-(b)(10)+(10)^2]
\\\\=
ab(b+10)(b^2-10b+100)
.\end{array}