Using mathematical induction on natural numbers to show ∀n. 0+2+4+...+2·n = n·(n+1)

Question

I'm working through a practice problem and have the solution but don't understand how the rearranging happens:

I have: \begin{align*} \ldots &= \big(n(n+1)\big) + 2(n+1) \\ &= (n + 2)(n + 1)\end{align*}

What is actually happening to get from the first line to the next one?

Answer 1

Hint: $$a\cdot b + c \cdot a = a\cdot (b+c)$$ for every $a,b,c \in \Bbb R$.

Answer 2

$\color{blue}{n}\color{red}{(n+1)} + \color{blue}{2}\color{red}{(n+1)} = \color{blue}{(n+2)}\color{red}{(n+1)}$