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Math Help - Binomial Theorem or Binomial Coefficient

  1. #1
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    Unhappy Binomial Theorem or Binomial Coefficient

    I hope this is the right part of the forum for this question.

    In the expansion of (1+ax)^4, the coefficient of x^3 is 1372. Find the constant a.

    Please Help !!
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  2. #2
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    (1+ax)^4 = \sum_{n=1}^{4} \binom{4}{n}a^nx^n

    So the coefficient of x^3 is \binom{4}{3}a^3

    Can you solve this now?
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  3. #3
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    By the binomial expansion, 4a^{3}=1372.

    Solve for a.

    Understand the pattern. a^{4}x^{4}+4a^{3}x^{3}+6a^{2}x^{2}+4ax+1
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  4. #4
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    Thanks, i got it now, i had to equate the 4C3 part of the expansion to 1372x^3

    Thanks
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