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In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem to polynomials. ==Theorem== 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'': : is a multinomial coefficient. The sum is taken over all combinations of nonnegative integer indices ''k''1 through ''k''''m'' such that the sum of all ''k''i is ''n''. That is, for each term in the expansion, the exponents of the ''x''''i'' must add up to ''n''. Also, as with the binomial theorem, quantities of the form ''x''0 that appear are taken to equal 1 (even when ''x'' equals zero). In the case ''m'' = 2, this statement reduces to that of the binomial theorem. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「multinomial theorem」の詳細全文を読む スポンサード リンク
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