Answer
$-5a^{2}b^{2}(a+b)(2a-5b)$
Work Step by Step
$-10a^{4}b^{2}+15a^{3}b^{3}+25a^{2}b^{4}\qquad$...factor out the common term, $-5a^{2}b^{2}$.
$=-5a^{2}b^{2}(2a^{2}-3ab-5b^{2})$
... Searching for two factors of $ac=-10$ whose sum is $b=-3,$
we find$\qquad 2$ and $-5.$
Rewrite the middle term and factor in pairs:
$=-5a^{2}b^{2}(2a^{2}+2ab-5ab-5b^{2})=$
$=-5a^{2}b^{2}[2a(a+b)-5b(a+b)]$
=$-5a^{2}b^{2}(a+b)(2a-5b)$