Show that $(n - 1)2^{n+1} + 2 + (n+1)2^{n+1} = n(2^{n+2})+2$ I'm having a really hard time showing this equality is true, I've tried several ways of going about it and I just can't seem to make it work. Help!
$(n - 1)2^{n+1} + 2 + (n+1)2^{n+1} = n(2^{n+2})+2$
Thanks!

$$\begin{align}\color{darkred}{\bf(n - 1)}\color{blue}{\bf 2^{n+1}} + 2 + \color{darkred}{\bf (n+1)}\color{blue}{\bf 2^{n+1}} & = \color{darkred}{\bf(n - 1 + n+1)}\color{blue}{\bf 2^{n+1}} + 2 \\ \\
& = 2n\cdot2^{n+1} +2 \\ \\ 
& = n\cdot 2\cdot 2^{n+1} + 2 \\ \\
& = n\cdot 2^{n+2} + 2 \\ \\
\end{align}$$
