What does: n(n+1) + 2(n+1) simplify to

I'm in a discrete math course covering Mathematical Induction but haven't done math in four years and my algebra is weak. I know that:

(n(n+1) + 2(n+1)) / 2

simplifies to:

(n+1)(n+2) / 2

but I cannot for the life of me figure out how it does it and I have many similar situations where I need to simplify but I cannot figure out where to go and I get stuck.

I need to know WHY this simplifies like this so that I can know how to do it in the future. Best answer goes to the explanation of WHY or HOW it works.

Also, does anyone know the name of the concept(s) dealing with this (e.g. "distributive property")?

Thank you.

There are a couple of ways to do this. One way is to factor out the common factor of n + 1 from the numerator, yielding:
n(n + 1) + 2(n + 1) = (n + 1)(n + 2),

as required.

The other way is to expand the numerator out to get:
n(n + 1) + 2(n + 1) = n^2 + 3n + 2.

Then, this factors to (n + 1)(n + 2).

I hope this helps!

(n^2 +n +2n + 2)/2.
{n(n+1)+2(n+1)}/2.
{(n+1)(n+2)}/2