Factor 3x^2y^2 − 2xy^2 − 8y^2. show your work.

3x^2y^2 − 2xy^2 − 8y^2 =
y^2 (3x^2 - 2x - 8) =

factoring with leading coefficient:

for ax2+bx+c find two numbers n,m, that m*n = a*c and m+n = b

3x^2 - 2x - 8
a=3, b=-2, c=-8
a*c = 3*(-8) = -24
-24=(-6)*4 and -6+4=-2, so m=-6 and n=4

replace bx with mx + nx and factor by grouping

3x^2 - 2x - 8 = 3x^2 -6x + 4x -8 = 3x(x-2) + 4(x-2) = (3x+4)(x-2)

3x^2y^2 − 2xy^2 − 8y^2 = y^2(3x+4)(x-2)