Prove by mathematical induction that $1^3+2^3+...n^3=1/4(n^2(n+1)^2)$

Question

In my attempt I arrived at $1/4(k^2(k+1)^2+4(k+1)^3)$ and don't know how to make any progress from there. I'm supposed to go from there to $(1/4(k+1)^2(k+2)^2)$ but have no idea how.

Answer 1

Factor $(k+1)^2$ out of $k^2(k+1)^2+4(k+1)^3$.

You will find that it is $(k+1)^2(k^2+4k+4)$ which further simplifies to $(k+1)^2(k+2)^2$