The multi- (or poly-) nomial theorem has for its object the expansion of any power of a multinomial and was discussed in 1697 by Abraham Demoivre (see Combinatorial Analysis).

If we expand the symbolic expression by the multinomial theorem, and remember that any symbolic product ai 1 a2 2 a3 3 ...

An expression denoting that two or more monomials are to be added or subtracted is a multinomial or polynomial, each of the monomials being a term of it.

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A multinomial consisting of two or of three terms is a binomial or a trinomial.