Hi Josh,
Factoring is an art. A large part of it is pattern recognition. It's like hearing the first few notes of a song you haven't heard before. You may not immediately know what group it is but if you have enough experience listening to similar music you have a pretty good idea who it is.
With enough experience factoring, hopefully you see
m^{4}  9^{n}
and think, this looks almost like a difference of squares. The complication here is the n may not be even so how can it be a difference of squares? But 9 is a square, 9 = 3^{2} . Thus you can rewrite the problem
m^{4}  9^{n} = m^{4}  (3^{2})^{n} = m^{4}  3 ^{2n} = m^{4}  3 ^{n2} = m^{4}  (3^{n})^{2}
Can you factor it now?
Penny
