# Math Help - SIMPLIFYING!! (ready for Binomial Expansion)

1. ## SIMPLIFYING!! (ready for Binomial Expansion)

I need to do binomial expansion on this:

(4-x) / √(1+2x)

which I've written as (4-x).(1+2x)^½

How do i simplyfy it so I get it in the form (1+x)^n

Am I being stupid or what!?

2. Originally Posted by liverpoolrdbest
I need to do binomial expansion on this:

(4-x) / √(1+2x)

which I've written as (4-x).(1+2x)^½

How do i simplyfy it so I get it in the form (1+x)^n

Am I being stupid or what!?
You could do this. Let $u = 2x$ so your expression is

$\frac{4-\frac{u}{2}}{\sqrt{1+u}} = \frac{1}{2} \frac{8-u}{\sqrt{1+u}} = \frac{1}{2} \;\frac{9 -1 - u}{\sqrt{1+u}} = \frac{9}{2} (1+u)^{-1/2} - \frac{1}{2}(1+u)^{1/2}$

then use a binomial expansion for each separately then multiply by the fraction out front, then substract, then replace u with 2x.