## binomial theoremA method of expanding the binomial expression ( x + y)^{n} into a finite or infinite series
of powers of x and y, where n is a number either
integral or fractional, positive or negative, rational
or irrational; thus x + y)^{n} = x^{n}
+ a_{n-1}x^{n-1}y +
a_{n-2}x^{n-2}y^{2}
+ ... + y^{n}
The coefficients a are called binomial
coefficients. _{i}The binomial theorem was discovered by Isaac Newton about 1666, and was first published in 1704 in the second appendix to Newton's Optics. That particular case of the theorem when n is
a positive integer was known to mathematicians prior to Newton (e.g., Briggs
and Pascal), and Newton himself gave no demonstration
of the truth of his theorem. ## Related category• COMBINATORICS | |||||

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