Mersenne Prime Proof

well i was trying to proof that 2^p -1 can only be prime if p is also a prime.
so p=r*s

2^(r*s) - 1 = (2^r)^s-1=(2^r-1)((2^r)^(s-1)+(2^r)^(s-2)+...+2r+1)
how was this step done?
 

Which step, the last?

x^n - 1 = (x - 1)(x^[n-1] + x^[n-2] + ... + x + 1)

Just start multiplying it out, to see it.

Aren't there a few exceptions to this?

>>3
If you mean a few exceptions to "2^p - 1 is prime if p is prime" yes, 2^11 - 1 isn't prime. However, it is true that (2^p - 1) is prime only if p is prime.