Understanding the Distributive Property: (n+1)^n(n+1)+1=n(n+1)^n+(n+1)^n+1

[Fabrizio]

Homework Statement

understanding the following equation:

$(n+1)^n(n+1)+1=n(n+1)^n+(n+1)^n+1$.

I don't know from where the first $n$ on the RHS comes and how this is related to a single addition of $(n+1)^n$.

Homework Equations

$a(b+c)=ab+ac$

The Attempt at a Solution

My guess is that it has something to do with the distributive property or the binomial theorem, but i don't see how. The fact that this is very basic, i don't know how to attack the problem. I don't know of any intermediate steps. If someone wants to point out an intermediate step, it would be very much appreciated.

 

[axmls]

Hint: distribute the second term in parenthesis to the first term.

 

[Fabrizio]

Aaaah, now i see it. I can't believe i did not notice it earlier. Thanks for the hint!