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?
I think there is no advantage here in expressing as negative powers. I did hope that the OP would give it a try first, and work on the numerator as suggested, using the common factor given, and that he would have picked up on the fact that he had not included the denominator in the full expression.
I didn't include the denomonator from the problem as it wasn't part of the issue I was having. When I took the 256(t-4)^7 * (7t+44) and used that, I got the problem right.
So my problem is converting
16(2t-8)^7 * (t+5 ) - (2t-8)^8 to 256(t-4)^7 * (7t+44)
So I'd bring out (2t-8)^7 and have
(2t-8)^7 * (16(t+5) - (2t-8))
working in the right side it'd be 16t+80-2t+8 or (2t-8)^7(14t+88)...can bring out a 2, so (2t-8)^7*2(7t+44)
Doesn't explain that 256 to me yet, am I still on the right track or did I muck up in my algebra again?