binomial

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binomial

(bī'nō`mēəl), polynomial expression (see polynomialpolynomial,
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 a0xn+a1x
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) containing two terms, for example, x+y. The binomial theorem, or binomial formula, gives the expansion of the nth 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=x5+5x4y+10x3y2+10x2y3+5xy4+y5. 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 PascalPascal, 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.
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), formed by adding adjacent numbers to find the number below them as follows:

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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 3x + 2y
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
References in periodicals archive ?
The semantic relationships between the components in the binomials in The Schoole can be divided into synonymy (example 48), antonymy (example 49), and contiguity (examples 50 and 51).
Keywords: Dengue Fever, Principal component analysis, Negative Binomial Model.
The Wald method has also been used in dealing with linear functions which involve binomial proportions, also known as binomial families.
First, various phonological constraints condition the optimal ordering of binomial pairs, and findings from our corpus investigations show that male names contain those features which lend them to be preferred in first position, while female names contain features which lend them to be preferred in second position.
We also discuss recent proposals to introduce a nonlatinized binomial nomenclature for virus species.
Subsequently, the next three hours were spent expanding binomials and factorising quadratic expressions with the vertically and crosswise method.
The scientific and infectious disease communities would benefit from the adoption of a standard pronunciation of Latin binomials that would obviate confusion and ambiguities.
Early in the study of algebra, students learn about binomials and begin to perform arithmetic operations with these binomials.
In order to deal with this issue we also estimate a negative binomial with commune fixed effect estimation and an OLS fixed effect.
The probability density functions for the Bernoulli and binomial distributions are given in Appendix A.