I'm reading through a number theory text and the following equivalence is used in a proof. It looks kind of like a binomial expansion, but not. I don't understand why this is true.
$a^n - 1= (a-1)(a^{n-1}+a^{n-2}+ \cdots + 1)$
Edit:
For the record, I can multiply. I'm curious to know why generally this is true, and how you get from $a^n -1$ to the above.
Okay, really what I'm asking, is how do you uncollapse a geometric series? Since that's what the right side of the equation is right? Is there a general method to do this?