Binomial And Multinomial Theorem. If x1 x2 are real numbers and nis a positive integer then. There are two proofs of the multinomial theorem an algebraic proof by induction and a combinatorial proof by counting.
N r n n r special cases. We have also previously seen how a binomial squared can be expanded using the distributive law. N 0 n n 1 n 1 n n 1 n binomial theorem.
X y n xn r 0 n r xryn r combinatorial interpretations.
N r represents 1. Proceed by induction on m. That is for each term in the expansion the exponents of the x i must add up to n. In statistics the corresponding multinomial series appears in the multinomial distribution which is a generalization of the binomial distribution.
