Answer
$3(x+y)(8x-9y)$
Work Step by Step
$ 24x^{2}+3xy-27y^{2}\qquad$...factor out the common term, $3$.
$=3(8x^{2}+xy-9y^{2})$
... ... Searching for two factors of $ac=-72$ whose sum is $b=1,$
we find$\qquad 8$ and $-9.$
Rewrite the middle term and factor in pairs:
$=3(8x^{2}+8xy-9xy-9y^{2})=$
$=3[8x(x+y)-9y(x+y)]$
= $3(x+y)(8x-9y)$
