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

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)
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