Multinomial Theorem Example. Left x 1 x 2 cdots x k right n sum b 1 b 2 cdots b k n binom n b 1 b 2 b 3 ldots b k prod j 1 k x j b j. For example in the bottom n 5 expansion the coefficients 1 5 10 10 5 and 1 add up to 2 5 32.
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Left x 1 x 2 cdots x k right n sum b 1 b 2 cdots b k n binom n b 1 b 2 b 3 ldots b k prod j 1 k x j b j.
For example in the bottom n 5 expansion the coefficients 1 5 10 10 5 and 1 add up to 2 5 32. Nk such that n1 n2. Displaystyle 3 choose 2 0 1 frac 3 2 cdot 0 cdot 1 frac 6 2 cdot 1 cdot 1 3. The coefficients in each expansion add up to 2 n.
