# binomial

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## binomial

(bī'nō`mēəl), polynomial expression (see polynomial**polynomial,**

mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is

*a*

_{0}

*x*

^{n}+

*a*

_{1}

*x*

**.....**Click the link for more information. ) containing two terms, for example,

*x*+

*y.*The binomial theorem, or binomial formula, gives the expansion of the

*n*th power of a binomial (

*x*+

*y*) for

*n*=1, 2, 3, … , as follows:

where the ellipsis (…) indicates a continuation of terms following the same pattern. For example, using the formula and reducing fractions, one obtains (

*x*+

*y*)

^{5}=

*x*

^{5}+5

*x*

^{4}

*y*+10

*x*

^{3}

*y*

^{2}+10

*x*

^{2}

*y*

^{3}+5

*x*

*y*

^{4}+

*y*

^{5}. The coefficients 1,

*n, n*(

*n*−1)/1·2, etc., of

*x*and

*y*may also be found from an array known as Pascal's triangle (for Blaise Pascal

**Pascal, Blaise**

, 1623–62, French scientist and religious philosopher. Studying under the direction of his father, a civil servant, Pascal showed great precocity, especially in mathematics and science.

**.....**Click the link for more information. ), formed by adding adjacent numbers to find the number below them as follows:

The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/

## binomial

[bī′nō·mē·əl] (mathematics)

A polynomial with only two terms.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## binomial

**1.**a mathematical expression consisting of two terms, such as 3

*x*+ 2

*y*

**2.**a two-part taxonomic name for an animal or plant

**3.**referring to two names or terms

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

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