Binomial Theorem Definition

noun
The theorem that specifies the expansion of any power ( a + b ) m of a binomial ( a + b ) as a certain sum of products aibj , such as ( a + b )2 = a2 + 2 ab + b2 .
American Heritage
The general formula for the expansion of any binomial when raised to a power that is a positive whole number; the expansion of (a + b)n: discovered by Omar Khayyám and generalized by Sir Isaac Newton (Ex.: (a + b)2 = a2 + 2ab + b2)
Webster's New World

(mathematics) A formula giving the expansion of a binomial such as raised to any positive integer power, i.e. . It's possible to expand the power into a sum of terms of the form where the coefficient of each term is a positive integer. For example.

Wiktionary

Binomial Theorem Sentence Examples

  • With Descartes the use of exponents as now employed for denoting the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected.

  • The binomial theorem gives a formula for writing down the coefficient of any stated term in the expansion of any stated power of a given binomial.

  • This is the binomial theorem for a positive integral index.

  • The binomial theorem for positive integral index may then be written (x + y) n = -iyi +.

  • If we represent this expression by f (x), the expression obtained by changing x into x-+-h is f(x+h); and each term of this may be expanded by the binomial theorem.

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Words Starting With

BBIBIN

Words Ending With

MEMREM

Unscrambles

binomial theorem

Words Starting With B and Ending With M

Starts With B & Ends With MStarts With BI & Ends With MStarts With B & Ends With EM

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