binomial theorem

English

(mathematics) 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 $ax^{b}y^{c}$ where the coefficient of each term is a positive integer. For example:
$(x+y)^{4}\;=\;x^{4}\,+\,4x^{3}y\,+\,6x^{2}y^{2}\,+\,4xy^{3}\,+\,y^{4}.$

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)
Finnish: binomilause
German: Binomialtheorem n, binomischer Lehrsatz m
Icelandic: tvíliðusetning f
Swedish: binomialsats c

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