1. Problem with higher powers

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?

2. Originally Posted by Wolvenmoon

There's a trick somewhere, what is it?
1. The "trick" is to find a common factor, which is the least power of the bracketed part, so that is (2t-8)^7. You do the rest.

2. Isn't there a denominator for this derivative?

3. Originally Posted by Wolvenmoon
The original problem: derive (2T-8)^8/(T+5)
You are on the right track

$\displaystyle \frac{16(2t-8)^7 \times (t+5 ) - (2t-8)^8\times 1}{(t+5 )^2}$

$\displaystyle 16(2t-8)^7 \times (t+5 )\times (t+5)^{-2} - (2t-8)^8\times 1\times (t+5)^{-2}$

Now clean it up a bit and take out any common factors.

4. 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.

5. 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?

6. Originally Posted by Wolvenmoon
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?
No, you didn't mess up, you just didn't finish the problem.

So you have $\displaystyle 2(2t-8)^7(7t+44) =$

$\displaystyle 2 \cdot 2^7 \cdot (t-4)^7 \cdot (7t+44) =$

$\displaystyle 256(t-4)^7(7t+44)$

7. I have to take up typing! Iceman beat me to it while I was busy wearing out my fingers.