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Homework Help: Series expansion/algebra problem

  1. Apr 26, 2014 #1

    i'm revising series expansions and my problem has arisen from an example in my text book, but it's not directly related to the series expansion itself. It's more of an algebra question, where they've made a rearrangement I can't follow...

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

    If [itex]n[/itex] is a positive integer find the coefficient of [itex]x^{r}[/itex] in the expansion of [itex](1 + x)(1 - x)^{n}[/itex] as a series of ascending powers of x.

    2. Relevant equations

    3. The attempt at a solution

    The solution starts by stating the following expressions are equivalent.

    [itex](1 + x)(1 - x)^{n} \equiv (1 - x)^{n} + x(1 - x)^{n}[/itex]

    If I take this statement to be true, I can follow through the rest of the example without a hitch, but I just can't see what they've done here.

    Thanks for any help you can give,

  2. jcsd
  3. Apr 26, 2014 #2
    Let ##(1-x)^n=a##, then ##a(1+x)=a+ax##. Do you see now? :)
  4. Apr 26, 2014 #3

    Thank you!
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