Binomial

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Binomial

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::$a^2 - b^2 = \left(a + b\right)\left(a - b\right).$(This is a special case of the more general formula $a^\left\{n+1\right\} - b^\left\{n+1\right\} = \left(a - b\right)sum_\left\{k=0\right\}^\left\{n\right\} a^\left\{k\right\},b^\left\{n-k\right\}$.)

The product of a pair of linear binomials "a x + b" and "c x + d" is::$\left(a x + b\right)\left(c x + d\right) = a c x^2 + \left(a d + b c\right) x + b d.$

A binomial raised to the "nth" power, represented as:$\left(a + b\right)^n$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 < n", let $a=n^2-m^2, b=2mn, c=n^2+m^2$, then $a^2+b^2=c^2$.

*Completing the square
*Binomial distribution
*Binomial coefficient
* Binomial-QMF (Daubechies Wavelet Filters)
*The list of factorial and binomial topics contains a large number of related links.

* [http://www.allmathwords.org/binomial.html Binomial] All Math Words Encyclopedia for grades 7-10.

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• binomial — binomial, iale, iaux [ binɔmjal, jo ] adj. • mil. XVe; de binôme ♦ Math. Relatif au binôme. Coefficient binomial : coefficient de la formule du binôme de Newton. Loi binomiale : loi de statistique d un phénomène à deux événements complémentaires… …   Encyclopédie Universelle

• Binomial — Bi*no mi*al, a. 1. Consisting of two terms; pertaining to binomials; as, a binomial root. [1913 Webster] 2. (Nat. Hist.) Having two names; used of the system by which every animal and plant receives two names, the one indicating the genus, the… …   The Collaborative International Dictionary of English

• Binomial — Bi*no mi*al, n. [L. bis twice + nomen name: cf. F. binome, LL. binomius (or fr. bi + Gr. ? distribution ?). Cf. {Monomial}.] (Alg.) An expression consisting of two terms connected by the sign plus (+) or minus ( ); as, a + b, or 7 3. [1913… …   The Collaborative International Dictionary of English

• binomial — Que contiene dos nombres o términos. Diccionario Mosby Medicina, Enfermería y Ciencias de la Salud, Ediciones Hancourt, S.A. 1999 …   Diccionario médico

• binomial — distribution …   Dictionary of sociology

• Binomial — distribution …   Dictionary of sociology

• binomial — 1550s (n.); 1560s (adj.), from L.L. binomius having two personal names, a hybrid from bi (see BI (Cf. bi )) + nomius, from nomen (see NAME (Cf. name)). Taken up 16c. in the algebraic sense consisting of two terms …   Etymology dictionary

• binomial — ► NOUN 1) Mathematics an algebraic expression of the sum or the difference of two terms. 2) Biology the two part Latin name of a species (the genus followed by the species name). ► ADJECTIVE ▪ consisting of two terms. ORIGIN from Latin bi having… …   English terms dictionary

• binomial — [bī nō′mē əl] n. [< ModL binomium < LL binomius < L bi , BI 1 + Gr nomos, law (see NOMY) + AL] 1. a mathematical expression consisting of two terms connected by a plus or minus sign 2. a two word scientific name of a plant or animal,… …   English World dictionary

• binomial — n. & adj. n. 1 an algebraic expression of the sum or the difference of two terms. 2 a two part name, esp. in taxonomy. adj. consisting of two terms. Phrases and idioms: binomial classification a system of classification using two terms, the first …   Useful english dictionary