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!?
Many thanks in advance
You could do this. Let $\displaystyle u = 2x$ so your expression is
$\displaystyle \frac{4-\frac{u}{2}}{\sqrt{1+u}} = \frac{1}{2} \frac{8-u}{\sqrt{1+u}} = \frac{1}{2} \;\frac{9 -1 - u}{\sqrt{1+u}} = \frac{9}{2} (1+u)^{-1/2} - \frac{1}{2}(1+u)^{1/2}$
then use a binomial expansion for each separately then multiply by the fraction out front, then substract, then replace u with 2x.