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Binomial Expansion long division

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

    Using the identity (1+2x) (1-2x+4x^2) = 1+8x^3 to expand (1-2x+4x^2)^(-0.5) in ascending powers of x as far as the term in x^3. (The answer is 1+x-x^2/2-7x^3/2+...)

    2. Relevant equations

    (1+2x)^(0.5) = 1+x-x^2/2+x^3/2+...
    (1+8x^3)^(-0.5) = 1-4x^3+...

    3. The attempt at a solution

    By long division, I have the solution of 1-x+3x^2/2-13x^3/2+...
  2. jcsd
  3. Mar 1, 2009 #2
    Since you have raised (1+2x) to the power of +(0.5), you should
    be multiplying, not dividing. (Easy).
  4. Mar 1, 2009 #3
    Yes, I got it.

    I forgot (1/(1+2x))^(-0.5) = (1+2x)^0.5.

    Thank you very much!
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