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In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: First ("first" terms of each binomial are multiplied together)
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 ...
A binomial raised to the n th power, represented as (x + y) n can be expanded by means of the binomial theorem or, equivalently, using Pascal's triangle. For example, the square (x + y) 2 of the binomial (x + y) is equal to the sum of the squares of the two terms and twice the product of the terms, that is:
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 ...
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution , not a binomial one.
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.
In taxonomy, binomial nomenclature ("two-term naming system"), also called binary nomenclature, is a formal system of naming species of living things by giving each a name composed of two parts, both of which use Latin grammatical forms, although they can be based on words from other languages.
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 ...