AskDefine | Define binomial

Dictionary Definition

binomial adj
1 relating to binomials; "binomial expression"
2 consisting of two names or terms; "binomial nomenclature" n : a quantity expressed as a sum or difference of two terms

User Contributed Dictionary

English

Etymology

binōminis (having two names)

Adjective

binomial
  1. Consisting of two names, terms, or parts.

Translations

  • Italian: binomiale

Noun

  1. A polynomial with two terms.
  2. A quantity expressed as the sum or difference of two terms.
  3. In the context of "biology|taxonomy": A scientific name at the rank of species, with two terms: a generic name and a specific name.
    • Usage note: Some people deprecate use of binomial and advocate use only of binominal in this context.
    • See species name for typesetting usage and example.

Synonyms

Translations

Extensive Definition

In elementary algebra, a binomial is a polynomial with two terms: the sum of two monomials. It is the simplest kind of polynomial except for a monomial.
The binomial a^2 - b^2 can be factored as the product of two other binomials:
a^2 - b^2 = (a + b)(a - b).
(This is a special case of the more general formula a^ - b^ = (a - b)\sum_^ a^\,b^.)
The product of a pair of linear binomials a x + b and c x + d is:
(a x + b)(c x + d) = a c x^2 + (a d + b c) x + b d.
A binomial raised to the nth power, represented as
(a + b)^n
can be expanded by means of the binomial theorem or, equivalently, using Pascal's triangle.

Example

A simple but interesting application of the cited binomial formula is the "(m,n)-formula" for generating Pythagorean triples: for ''m a=n^2-m^2,\ b=2mn,\ c=n^2+m^2, then a^2+b^2=c^2.
binomial in Catalan: Binomi
binomial in Hebrew: נוסחאות הכפל המקוצר
binomial in German: Binom
binomial in Estonian: Binoom
binomial in Spanish: Igualdades notables
binomial in Esperanto: Vikipedio:Projekto matematiko/Dutermo
binomial in French: Binôme (mathématique)
binomial in Italian: Binomio
binomial in Polish: Dwumian
binomial in Slovenian: Binom
binomial in Swedish: Binom
binomial in Finnish: Binomi
binomial in Ukrainian: Біном
binomial in Chinese: 二项式
binomial in Dutch: Merkwaardig product
and also a binomial is a polynomial that has two term. You can use the distributive property to find the prduct of the monimial and a binomial.

Synonyms, Antonyms and Related Words

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