How do I prove this by induction?

Prove that for every natural number n, $ 2^0 + 2^1 + ... + 2^n = 2^{n+1}-1$

Here is my attempt.

Base Case: let $ n = 0$ Then, $2^{0+1} - 1 = 1$ Which is true.

Inductive Step to prove is: $ 2^{n+1} = 2^{n+2} - 1$

Our hypothesis is: $2^n = 2^{n+1} -1$

Here is where I'm getting off track. Lets look at the right side of the last equation: $2^{n+1} -1$ I can rewrite this as the following.

$2^1(2^n) - 1$ But, from our hypothesis $2^n = 2^{n+1} - 1$ Thus:

$2^1(2^{n+1} -1) -1$ This is where I get lost. Because when I distribute through I get this.

$2^{n+2} -2 -1$ This is wrong is it not? Am I not applying the rules of exponents correctly here? I have the solution so I know what I'm doing is wrong. Here is the correct proof.