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

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

• In the context of "biology|taxonomy}} binomen
• binominal
• species name

Translations

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.

See also

• Completing the square
• Binomial distribution
• Binomial coefficient
• The list of factorial and binomial topics contains a large number of related links.

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.

Linnaean, biaxial, bicameral, bicuspid, bifid, biform, binocular, binominal, bipartite, biped, bipetalous, bipinnate, bisexual, bivalent, classificatory, nomenclatural, onomastic, orismological, taxonomic, terminological, toponymic, toponymous, trinomial, unibivalent