FactoringDistributing Rules

[rockrock]

The Advanced section of the Number Properties book lists this factoring rule:

m^n - m^n-1 = m^n (1-m^-1) = m(^n-1)(m-1)
as an example
5^5 - 5^4 = 5^5(1 - 5^-1) = 5^5 (1 - 1/5) = 5^4(5-1)

I am assuming we are just being shown 2 different ways to factor: pulling out the 5^5 versus pulling out the 5^4. If this is correct, in what context would we have to "decide" factorization to use?

[tim]

My advice is not to worry about deciding. When you see a problem you know needs to be factored, use the first factoring trick that comes to mind. If that doesn't work (which will be very rare), see if you can come up with another factoring trick to use..