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

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)