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Math Help - Multinomial Expansion

  1. #1
    Senior Member pankaj's Avatar
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    Multinomial Expansion

    Find number of dissimilar terms in the expansion (1+ax^p+bx^q+cx^r)^n where p,q,r are different integers and n is a non-negative integers.(p,q,r may be either positive or negative and a,b,c are any real numbers)
    Does there exist a general formula?
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  2. #2
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    answer

    for the expansion of (t1+t2+...+tm-1+tm)^n there are
    (n+m-1)!/(n!*(m-1)!) terms as long as p, q, r do not equal 0. if so then simplify the expression and repeat this procedure from the beginning
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  3. #3
    Senior Member pankaj's Avatar
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    i am famaliar with this formula.but does it work in this case.For e.g. in expansion of (1-3x+7x^2)^n there are 2n+1 dissimilar terms.
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