Subject: factoring
Name: Josh
Who are you: Student

I can not figure out how to completely factor m^4-9^n. I am completely lost. Any help would be appreciated.

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

m⁴ - 9ⁿ

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 = 3² . Thus you can rewrite the problem

m⁴ - 9ⁿ = m⁴ - (3²)ⁿ = m⁴ - 3 ²ⁿ = m⁴ - 3 ⁿ² = m⁴ - (3ⁿ)²

Can you factor it now?

Penny