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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 from binomials to multinomials.
The multinomial theorem describes how to expand the power of a sum of more than two terms. It is a generalization of the binomial theorem to polynomials with any number of terms.
Multinomial Theorem. The Multinomial Theorem states that where is the multinomial coefficient . Note that this is a direct generalization of the Binomial Theorem, when it simplifies to.
Definition of Multinomial Theorem. The multinomial theorem is used to expand the sum of two or more terms raised to an integer power. The multinomial theorem provides a formula for expanding an expression such as \ (\left (x_ {1}+x_ {2}+\cdots+x_ {k}\right)^ {n}\), for an integer value of \ (n\).
In this lecture, we discuss the binomial theorem and further identities involving the binomial coe cients. At the end, we introduce multinomial coe cients and generalize the binomial theorem. Binomial Theorem. At this point, we all know beforehand what we obtain when we unfold (x + y)2 and (x + y)3.
In this article on the Multinomial Theorem, we will learn about what is Multinomial Theorem, the history of Multinomial Theorem, uses of Multinomial Theorem, operations on Multinomial Theorem, and many more in detail.
The multinomial theorem provides a formula for expanding an expression such as (x1 + x2 +⋯+ xk) n for integer values of n. In particular, the expansion is given by where n1 + n2 +⋯+ nk = n and n! is the factorial notation for 1 × 2 × 3 ×⋯× n.