Answer
$(2x+3)(2x-3)(3y-1)$
Work Step by Step
$12x^{2}y-27y-4x^{2}+9=$... factor in pairs
$=(12x^{2}y-27y)+(9-4x^{2})$... factor out -1 in the 2nd term
$=3y(4x^{2}-9)-1(4x^{2}-9)$
$=(4x^{2}-9)(3y-1)$
...The first parentheses hold a difference of squares $(2x)^{2}-(3)^{2}$
$=(2x+3)(2x-3)(3y-1)$
