This is really a simple (pre?)algebra issue, but this type of problem is causing me trouble over and over, so I want to understand and get to the heart of these types of problems.
I'm trying to simplify this equation as part of an inductive proof of a recurrence relation.
$5 \left(2^{k + 1} + 3^k\right) - 6 \left(2^k + 3^{k - 1}\right)$
I can run this through wolfram alpha and see it's equivalent to what I need, which is:
$2^{k+2}+3^{k+1}$
But I'm having trouble figuring out how to get there myself. Can someone break down the steps for me (and/or point me somewhere)? Thanks! [edit: fixed the k-1 to be k+1]