The original problem: derive (2T-8)^8/(T+5)
My hangup is here.
16(2t-8)^7 * (t+5 ) - (2t-8)^8
I should be able to do this but it's been a hard day and I'm having a nerve pinch in my shoulder, so I know the answer, from my calculator, is: 256(t-4)^7 * (7x+44) but I have no idea how I got there outside of a ridiculous amount of work expanding the binomials, combining like terms, and then factoring them back down.
There's a trick somewhere, what is it?