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Binomial Expansion

  1. Mar 21, 2009 #1
    1. The problem statement, all variables and given/known data

    (a) Expand (1-x6)4
    (b) Find the coefficient of xr, where r is a non-negative integer, in the expansion of (1-x)-4 for |x|<1.
    (c) Using (a) and (b), or otherwise, find the coefficient of x^8 in the expansion of ((1-x6)/(1-x))4 for |x|<1.

    (Answers:
    (a) 1-4x6+6x12-4x18+x24
    (b) (r+1)(r+2)(r+3)/6
    (c) 125)

    2. Relevant equations

    Binomial Expansion: n(n-1)...(n-r+1)*xr/r!

    3. The attempt at a solution

    I can solve parts (a) and (b) but not part (c).

    I tried (-4)(2+3)(2+2)(2+1)/6 = -40 but not correct.

    Can anyone tell me how to solve it?

    Thank you very much!
     
  2. jcsd
  3. Mar 21, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi chrisyuen! :smile:
    Yes, that's x6 times x2

    now what about 1 times x8? :wink:
     
  4. Mar 21, 2009 #3
    Yes, I got it!

    Thank you very much!
     
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