Let n be a positive integer. Show that K=2^(2n-1)-9n^2+21n-14 is a multiple of 27.
To try to attempt solving this, I actually used a trial and error method where I plugged in various numbers just to see what I got. For instance, I did K(1), K(2), and K(3), but my answers were just 0. I'm sure there's an algebraic approach to this, but I need some guidance.