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Applying the binomial theorem

  1. Jul 25, 2013 #1

    reenmachine

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    1. The problem statement, all variables and given/known data

    Use the binomial theorem to find the coefficient of ##x^8y^5## in ##(x+y)^{13}##.

    2. Relevant equations

    We know 13 - 5 = 8 , so we have ##\binom{n}{5}x^{n-5}y^5 = \binom{13}{5}x^8y^5##

    ##\binom{13}{5} = \frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{5!8!} = \frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9}{120} = \frac{154440}{120} = 1287##

    So ##1287x^8y^5##

    This is the first time I work with the binomial theorem so I'm not sure , any thoughts on my result?

    thank you!
     
    Last edited: Jul 25, 2013
  2. jcsd
  3. Jul 25, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    I don't see why you introduced "n" there.
    The solution is right.
     
  4. Jul 25, 2013 #3

    reenmachine

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    sorry this was a brain cramp on my part.The book I'm reading introduced the binomial theorem as followed: If ##n## is a non-negative integer , then ##(x+y)^n = \binom{n}{0}x^n + \binom{n}{1}x^{n-1}y + \binom{n}{2}x^{n-2}y^2 + \binom{n}{3}y^3 + \cdots + \binom{n}{n-1}xy^{n-1}+\binom{n}{n}y^n##.For some reasons I forgot to connect ##n## to ##(x+y)^n## and ##\mathbb{N}##.

    thank you!!!
     
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