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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
The roots for the binomial name are crassus (thick, fat) and rupestris (living on cliffs or rocks) This list of Latin and Greek words commonly used in systematic names is intended to help those unfamiliar with classical languages to understand and remember the scientific names of organisms.
Binomial (polynomial), a polynomial with two terms; Binomial coefficient, numbers appearing in the expansions of powers of binomials; Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition; Binomial theorem, a theorem about powers of binomials; Binomial type, a property of sequences of polynomials; Binomial series, a ...
A binomial is a polynomial which is the sum of two monomials. A binomial in a single indeterminate (also known as a univariate binomial) can be written in the form , where a and b are numbers, and m and n are distinct non-negative integers and x is a symbol which is called an indeterminate or, for historical reasons, a variable.
The expression "macaroni and cheese" is an irreversible binomial.The order of the two keywords of this familiar expression cannot be reversed idiomatically.. In linguistics and stylistics, an irreversible binomial, [1] frozen binomial, binomial freeze, binomial expression, binomial pair, or nonreversible word pair [2] is a pair of words used together in fixed order as an idiomatic expression ...
Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written (). It is the coefficient of the x k term in the polynomial expansion of the binomial power (1 + x) n, and it is given by the formula =!! ()!.
A complete binomial name is always treated grammatically as if it were a phrase in the Latin language (hence the common use of the term "Latin name" for a binomial name). However, the two parts of a binomial name can each be derived from a number of sources, of which Latin is only one. These include:
This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms. Exponential function [ edit ]