Answer
$2a^{2}(4a-b)(3a+2b)$
Work Step by Step
Factor out the gratest common factor, $2a^{2}$
$=2a^{2}\left(12a^{2}+5ab-2b^{2}\right)$
When factoring $ax^{2}+bx+c$, we search for factors of $ac$ whose sum is $b,$
and, if we find them, we rewrite $bx$ and proceed to factor in groups.
Here, factors of $(12)\times(-2)=-24$ that add to $+5$ are ....$+8$ and $-3 .$
$=2a^{2}\left[ \left(12a^{2}-3ab\right)+\left(8ab-2b^{2}\right) \right]$
$=2a^{2}\left[ 3a(4a-b)+2b(4a-b) \right]$
$=2a^{2}\left[ (4a-b)(3a+2b) \right]$
$=2a^{2}(4a-b)(3a+2b)$
