Question

How do I factor the following, if possible? You don't have to answer all, I just need to know how.

27f^2g^2 + 18f^2g^3 - 3f^2g

Answer 1

remember
ab+ac=a(b+c)
find common factors

factor each to find a
27f^2g^2=3*3*3*f*f*g*g
18f^2g^3=2*3*3*f*f*g*g*g
-3f^2g=-1*3*f*f*g

common group is
3*f*f*g=3f^2g
so rewrite as
3f^2g(9g)+3f^2g(6g^2)+3f^2g(-1)
undistribute
(3f^2g)(9g+6g^2-1)
rearange inner
(3f^2g)(6g^2+9g-1)