I am completely aware of what I need to be doing to prove something by induction, except my algebra skills are too crappy to do it.

For example

prove the following by induction...

1^3 + 2^3 + 3^3 + ... + n3 = n^2(n+1)^2/4

I have already proved this is the case for n=1 and n=2

Then I say suppose it holds for n=k where k>=1

k^2(k+1)^2/4

Then I have to show it holds for k+1

So I have to show that....

(k+1)^2[(k+1)+1]^2/4 = k^2(k+1)^2/4 + (k+1)^2

Is this correct?

If it is how do i even start here. I noticed that they both have a (k+1)^2 term so i started by pulling that out front. I just get so lost from there...