Binomial Theorem

(Theory)

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What is Binomial theorem?

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. For example (for n = 4), The coefficient a in the term of axbyc is known as the binomial coefficient or (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where gives the number of different combinations of b elements that can be chosen from an n-element set. Therefore is often pronounced as "n choose b".

Technology Types

factorial and binomial topicfunctionidentitymathematical identitymathematical relationmathematical theorempersonalitypolynomialpropositionstatementtheoremtheorems in algebratheorems in combinatorictheory

Synonyms

Binomial expansionBinomial expansion theoremBinomial expansionsBinomial formulaBinomial theoryCatalon seriesNegative binomial theoremNewton's binomial theoremNewton's generalized binomial theorem

Translations

Binomi de Newton (ca)Binomialsatsen (sv)Binomická věta (cs)Binómio de Newton (pt)Binomischer Lehrsatz (de)Binomium van Newton (nl)Binomo de Newton (eo)Dwumian Newtona (pl)Formule du binôme de Newton (fr)Newtonen binomio (eu)Teorema binomial (in)Teorema binomiale (it)Teorema del binomio (es)Бином Ньютона (ru)Біном Ньютона (uk)نظرية ذات الحدين (ar)이항 정리 (ko)二項定理 (ja)二项式定理 (zh)

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