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多项式定理为二项式定理的推广。 时为二项式定理。
其中 、
是指一切满足上述条件的非负数组合。
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.
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![t=2](/Images/godic/202501/28/b0af76257fd334f5200fa9c2a421688a4439.png")
时为二项式定理。![(x_1+x_2+...+x_t)^n=\sum\frac{n!}{n_1!n_2!...n_t!}x_1^{n_1}x_2^{n_2}...x_t^{n_t}](/Images/godic/202501/28/88e1b4e7d4b50d0dfd143139477398aa4439.png")
![n_1+n_2+...+n_t=n](/Images/godic/202501/28/f0abc679eb9d6bde8002aab105cc504a4439.png")
、![0\le n_i\le n](/Images/godic/202501/28/272cd55728efe4c08ff35cf451bbc47c4439.png")
![n_1,n_2, n_3 ... n_t](/Images/godic/202501/28/bed23dfc487eea317689b0244cbb03f54439.png")
是指一切满足上述条件的非负数组合。