binomial theorem

Noun

 * 1)  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:
 * $$(x+y)^4 \;=\; x^4 \,+\, 4 x^3y \,+\, 6 x^2 y^2 \,+\, 4 x y^3 \,+\, y^4.$$

Translations

 * Arabic: نَظَرِيَّةُ ذَاتِ الْحَدَّيْنِ, مُبَرْهَنَةُ ذَاتِ الْحَدَّيْنِ, نَظَرِيَّةُ ذِي الْحَدَّيْنِ, مُبَرْهَنَةُ ذِي الْحَدَّيْنِ, نَظَرِيَّةُ الثُّنَاحَدِّيِّ, مُبَرْهَنَةُ الثُّنَاحَدِّيِّ
 * Finnish: binomilause
 * German: Binomialtheorem, binomischer Lehrsatz
 * Icelandic: tvíliðusetning
 * Swedish: binomialsats