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

  1. #1
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    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)^

    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
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  2. #2
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    Quote Originally Posted by liverpoolrdbest View Post
    I need to do binomial expansion on this:

    (4-x) / √(1+2x)

    which I've written as (4-x).(1+2x)^

    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 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.
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