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Binomial Theorem For Quadratic Equation

  1. Jul 24, 2008 #1

    Air

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    Question:
    Find the coefficient of [itex]x^5[/itex] in [itex](1+x+x^2)^4[/itex].


    Problem:
    I have not come across expanding brackets which have [itex]x^2[/itex]. I know how to apply the binomial theorem for [itex](a+b)^n[/itex] or [itex](1+a)^n[/itex] but have not come across [itex](1 + ax + ax^2)^n[/itex]. They are not explained in my textbooks so I was wondering if you could provide hints or redirect me to a useful link. Thanks.
     
  2. jcsd
  3. Jul 24, 2008 #2

    rock.freak667

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    Homework Helper

    Just use [itex]b=x+x^2[/itex] and if you need to expand out [itex]b^2,b^3,b^4[/itex] just use the terms that will give you [itex]x^5[/itex]
     
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