# binomial theorem

The binomial theorem is a 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 _{i}* are called binomial
coefficients.

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.