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!? (Wondering)

Many thanks in advance

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- Jan 24th 2009, 12:41 PMliverpoolrdbestSIMPLIFYING!! (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!? (Wondering)

Many thanks in advance - Jan 24th 2009, 01:20 PMJester
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.