Binomial theorem

binomial theorem
    n 1: a theorem giving the expansion of a binomial raised to a
         given power
    

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.
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            Not theories, but theorems (?), the intelligible
            products of contemplation, intellectual objects in
            the mind, and of and for the mind exclusively.
                                                  --Coleridge.
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            By the theorems,
            Which your polite and terser gallants practice,
            I re-refine the court, and civilize
            Their barbarous natures.              --Massinger.
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   2. (Math.) A statement of a principle to be demonstrated.
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   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.
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   {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.
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Binomial \Bi*no"mi*al\, a.
   1. Consisting of two terms; pertaining to binomials; as, a
      binomial root.
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   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.
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   {Binomial theorem} (Alg.), the theorem which expresses the
      law of formation of any power of a binomial.
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