how do you do binomial expansion when the power is a negative

There is a simple equation, similar to the normal binomial expansion, thats easy to remember once youve used it a few times.

(1+x)ⁿ=1+nx+{[n(n-1)]/2!}x²+{[n(n-1)(n-2)]/3!}x³+...

This looks complicated but once you plug in values for n its actually pretty straight forward. 

Lets say we have the equation (1+x)^-5 where -1d x=x. If we are asked to find the first 4 terms of this expansion we plug in the numbers up to the x³ term.

(1+x)^-5=1-5x+{[(-5)(-6)]/2}x²+{[(-5)(-6)(-7)]/6]}x³+...

           =1-5x+15x²-35x³+...

There are trickier examples when x has a co-efficent larger than 1 or when the the number term in the bracket is not 1 alone, but we can look at those examples later.