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!

$$a\cdot 2^{n+1} + b\cdot 2^{n+1} = (a+b)\cdot 2^{n+1}$$
by the distributive law. Now let $a=n-1$ and $b=n+1$. Then $a+b=2n$.
