binomial theorem

English

Noun

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binomial theorem

Wikipedia

binomial theorem

1. (mathematics) A formula giving the expansion of a binomial such as ${\displaystyle (a+b)}$ raised to any positive integer power, i.e. ${\displaystyle (a+b)^{n}}$. It's possible to expand the power into a sum of terms of the form ${\displaystyle ax^{b}y^{c}}$ where the coefficient of each term is a positive integer. For example:

   ${\displaystyle (x+y)^{4}\;=\;x^{4}\,+\,4x^{3}y\,+\,6x^{2}y^{2}\,+\,4xy^{3}\,+\,y^{4}.}$

Translations

formula giving the expansion of an alegraic sum raised to any positive integer power

Arabic: نَظَرِيَّةُ ذَاتِ الْحَدَّيْنِ f (naẓariyyatu ḏāti l-ḥaddayni), مُبَرْهَنَةُ ذَاتِ الْحَدَّيْنِ f (mubarhanatu ḏāti l-ḥaddayni), نَظَرِيَّةُ ذِي الْحَدَّيْنِ f (naẓariyyatu ḏī l-ḥaddayni), مُبَرْهَنَةُ ذِي الْحَدَّيْنِ f (mubarhanatu ḏī l-ḥaddayni), نَظَرِيَّةُ الثُّنَاحَدِّيِّ f (naẓariyyatu ṯ-ṯunāḥaddiyyi), مُبَرْهَنَةُ الثُّنَاحَدِّيِّ f (mubarhanatu ṯ-ṯunāḥaddiyyi) Chinese: Mandarin: 二項式定理 / 二项式定理 (zh) (èrxiàngshì dìnglǐ) Finnish: binomilause German: Binomialtheorem n, binomischer Lehrsatz m Icelandic: tvíliðusetning f Spanish: teorema del binomio m Swedish: binomialsats c