Prove the Binomial Theorem using Induction

I'm trying to prove the Binomial Theorem using induction. I know that I am supposed to use ${n\choose k} + {n\choose k - 1} = {n + 1 \choose k}$. I just really want to know how to use this equation for the inductive step. I've already verified that the base step of $n = 1$ is true.

Also, I'm not quite sure what the inductive hypothesis is for this theorem.

I appreciate any and all help on this inquiry.

Thank you in advance!

Answer

Hint: you write $(x+y)^{n+1}=(x+y)^n(x+y)$, then use the binomial formula for $(x+y)^n$ as induction hypothesis, expand and use the identity which you wrote.