How is: $(n+1)!(n+1)+(n+1) = (n+2)!$?

Question

i want to show that $(n+1)!(n+1)+(n+1)! = (n+2)!$

i put it into wolfram and it showed this to be true, but im not sure why.

I need to show this as a part of a induction proof.

Answer 1

Factor out the $(n+1)!$. Then use the fact that $(n+1)!(n+2)=\left(1(2)(3)..(n+1)\right)(n+2)=(n+2)!$.

Answer 2

Factor out $(n+1)!$ from both terms:

$$ (n+1)!\,(n+1)+(n+1)!=(n+1)!\left[(n+1)+1\right]=(n+1)!\,(n+2)=(n+2)! $$