'Binomial theorem' definitions:

Definition of 'binomial theorem'

noun

A theorem giving the expansion of a binomial raised to a given power

From: GCIDE

Theorem \The"o*rem\, n. [L. theorema, Gr. ? a sight, speculation, theory, theorem, fr. ? to look at, ? a spectator: cf. F. th['e]or[`e]me. See Theory.]
1. That which is considered and established as a principle; hence, sometimes, a rule. [1913 Webster]
Not theories, but theorems (?), the intelligible products of contemplation, intellectual objects in the mind, and of and for the mind exclusively. --Coleridge. [1913 Webster]
By the theorems, Which your polite and terser gallants practice, I re-refine the court, and civilize Their barbarous natures. --Massinger. [1913 Webster]
2. (Math.) A statement of a principle to be demonstrated. [1913 Webster]
Note: A theorem is something to be proved, and is thus distinguished from a problem, which is something to be solved. In analysis, the term is sometimes applied to a rule, especially a rule or statement of relations expressed in a formula or by symbols; as, the binomial theorem; Taylor's theorem. See the Note under Proposition, n., 5. [1913 Webster]
Binomial theorem. (Math.) See under Binomial.
Negative theorem, a theorem which expresses the impossibility of any assertion.
Particular theorem (Math.), a theorem which extends only to a particular quantity.
Theorem of Pappus. (Math.) See Centrobaric method, under Centrobaric.
Universal theorem (Math.), a theorem which extends to any quantity without restriction. [1913 Webster]

From: GCIDE

Binomial \Bi*no"mi*al\, a.
1. Consisting of two terms; pertaining to binomials; as, a binomial root. [1913 Webster]
2. (Nat. Hist.) Having two names; -- used of the system by which every animal and plant receives two names, the one indicating the genus, the other the species, to which it belongs. [1913 Webster]
Binomial theorem (Alg.), the theorem which expresses the law of formation of any power of a binomial. [1913 Webster]