Multinomial Theorem Expansion. The multinomial theorem provides a formula for expanding an expression such as x1 x2 xk n for integer values of n. Be the set of nonnegative integral solutions to the equation.
X1 x2 xm n σ r1. It expresses a power. Multinomials with 4 or more terms are handled similarly.
X1 x2 xm n σ n r1 rm 1.
X1 x2 xm n σ n r1 rm 1. How this series is expanded is given by the multinomial theorem where the sum is taken over n1 n2. In particular the expansion is given by where n1 n2 nk n and n. The multinomial theorem the multinomial theorem extends the binomial theorem.
