# Thread: Multinomial Expansion

1. ## 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?

2. ## 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

3. 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.

### multinomial exansin

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