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Math Help - Binomial Theorem and simplifying coefficient

  1. #1
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    Binomial Theorem and simplifying coefficient

    6. a) Find and simplify the coefficient of a^12*b^25 in the expression (a+b)^37.

    I've no clue how to separate this... it might have something to do with complex numbers as we are covering this topic but we did not do any examples like this.

    Please help.
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  2. #2
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    You use the binomial theorem
     (a+b)^n = \sum_{k=0}^n {n\choose k} a^k b^{n-k}.
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  3. #3
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    the coefficient of a^12*b^25 in the expansion of (a+b)^37 is
    37C25 where aCb=a!/b!(a-b)! and n!=n(n-1)(n-2).......3.2.1. we can easily simplify the coefficient. however it is a bit lengthy!.
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