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Can I ask for the proof of the Multinomial Theorem? Wikipedia says:

For any positive integer ''m'' and any nonnegative integer ''n'', the multinomial formula tells us how a sum with ''m'' terms expands when raised to an arbitrary power ''n'':

$$(x_1 + x_2 + \cdots + x_m)^n = \sum_{k_1+k_2+\cdots+k_m=n} {n \choose k_1, k_2, \ldots, k_m} \prod_{1\le t\le m}x_{t}^{k_{t}}\,,$$ where $$ {n \choose k_1, k_2, \ldots, k_m} = \frac{n!}{k_1!\, k_2! \cdots k_m!}$$ is a '''multinomial coefficient'''.

But I find the proof they provide on Wikipedia to be insufficiently too brief.

user164606
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  • http://math.stackexchange.com/questions/568973/combinatorial-proof-of-multinomial-theorem-without-induction-or-binomial-theor – Juanito Jul 16 '14 at 02:48
  • I dont want the combinatorial proof. I want the one that uses binomial theorem. Is there an existing page containing that? – user164606 Jul 16 '14 at 02:52
  • I haven't worked it out, but I would use the expression $((x_1+x_2+\dots+x_{m-1})+x_m)^n$, even with the binomial theorem, I think that you would still require a Combinatorics portion to the inductive proof. – John Joy Jul 17 '14 at 13:31

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