Factorize each of the following expression:

$75 a^{3} b^{2}-108 a b^{4}$

$=3 a b^{2}\left(25 a^{2}-36 b^{2}\right)$

$=3 a b^{2}\left[(5 a)^{2}-(6 b)^{2}\right]$

$=3 a b^{2}(5 a-6 b)(5 a+6 b)$