Multinomial synonyms

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

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.

In the same way we have (A-a) 2 =A 2 -2Aa+a 2, (A-a)3 = A 3 -3A 2 a+3Aa 2 -a 3, ..., so that the multinomial equivalent to (A-a)" has the same coefficients as the multinomial equivalent to (A+a)", but with signs alternately + and -.

The multinomial which is equivalent to (A= a)", and has its terms arranged in ascending powers of a, is called the expansion of (A= a) n.

We know that (A+a)" is equal to a multinomial of n+I terms with unknown coefficients, and we require to find these coefficients.