Question

Factor by removing the common factor with the lesser exponent
2x(x-5)^-3 -4x^2(x-5)^-4
I don't really know how to do this.
The final answer I got is:
2x(2x^2-10x+1)
--------------
(x-5)^4

Answer 1

2x(x-5)^-3(1-2x(x-5)^-1) =
2x/(x-5)^3 * (1-2x/(x-5)) =
2x/(x-5)^3 * ((x-5)/(x-5)-2x/(x-5) =
2x/(x-5)^3 * (-x-5)/(x-5) =
2x(-x-5))/(x-5)^4).

Answer 2

Take a look at what wolframalpha got:

http://www.wolframalpha.com/input/?i=2x+%28x-5%29^-3+-4x^2+%28x-5%29^-4