binomial theorem

proper noun

A formula giving the expansion of a binomial such as (a+b) raised to any positive integer power, i.e. (a+b)ⁿ. It's possible to expand the power into a sum of terms of the form axᵇyᶜ where the coefficient of each term is a positive integer. For example

“(x+y)⁴;=;x⁴,+,4x³ʸ,+,6x²y²,+,4xy³,+,y⁴.”

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Meanings

proper nounthe binomial theorem
  1. mathematicsA formula giving the expansion of a binomial such as (a+b) raised to any positive integer power, i.e. (a+b)ⁿ. It's possible to expand the power into a sum of terms of the form axᵇyᶜ where the coefficient of each term is a positive integer. For example

    (x+y)⁴;=;x⁴,+,4x³ʸ,+,6x²y²,+,4xy³,+,y⁴.

Translations

Arabic نَظَرِيَّةُ ذَاتِ الْحَدَّيْنِ, مُبَرْهَنَةُ ذَاتِ الْحَدَّيْنِ
  • نَظَرِيَّةُ ذَاتِ الْحَدَّيْنِ (naẓariyyatu ḏāti l-ḥaddayni)formula giving the expansion of an alegraic sum raised to any positive integer power
  • مُبَرْهَنَةُ ذَاتِ الْحَدَّيْنِ (mubarhanatu ḏāti l-ḥaddayni)formula giving the expansion of an alegraic sum raised to any positive integer power
  • نَظَرِيَّةُ ذِي الْحَدَّيْنِ (naẓariyyatu ḏī l-ḥaddayni)formula giving the expansion of an alegraic sum raised to any positive integer power
  • مُبَرْهَنَةُ ذِي الْحَدَّيْنِ (mubarhanatu ḏī l-ḥaddayni)formula giving the expansion of an alegraic sum raised to any positive integer power
  • نَظَرِيَّةُ الثُّنَاحَدِّيِّ (naẓariyyatu ṯ-ṯunāḥaddiyyi)formula giving the expansion of an alegraic sum raised to any positive integer power
  • مُبَرْهَنَةُ الثُّنَاحَدِّيِّ (mubarhanatu ṯ-ṯunāḥaddiyyi)formula giving the expansion of an alegraic sum raised to any positive integer power
Chinese Mandarin 二項式定理 /二项式定理
  • 二項式定理 /二项式定理 (èrxiàngshì dìnglǐ)formula giving the expansion of an alegraic sum raised to any positive integer power
Finnish binomilause
  • binomilauseformula giving the expansion of an alegraic sum raised to any positive integer power
German Binomialtheorem, binomischer Lehrsatz
  • Binomialtheoremformula giving the expansion of an alegraic sum raised to any positive integer power
  • binomischer Lehrsatzformula giving the expansion of an alegraic sum raised to any positive integer power
Icelandic tvíliðusetning
  • tvíliðusetningformula giving the expansion of an alegraic sum raised to any positive integer power
Spanish teorema del binomio
  • teorema del binomioformula giving the expansion of an alegraic sum raised to any positive integer power
Swedish binomialsats
  • binomialsatsformula giving the expansion of an alegraic sum raised to any positive integer power
Cite this entry
APA

binomial theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/binomial%20theorem

MLA

“binomial theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/binomial%20theorem. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “binomial theorem,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/binomial%20theorem.

Source: binomial theorem on Wiktionary, CC BY-SA 4.0.