Greetings, I've been trying to solve this question for quite some time now but I just can't figure it out.

I proved that it works for n=1, now what I need to do is:

Assuming that:

is true for every natural number, I need to prove it for n+1, like this:

So I need to prove that what's on the left is equal to the right. Using the assumption I get this:

So now I need to take whats on the left and make it look like what's on the right, does anyone know how to do it?

Thanks in advance.