There are several closely related results that are variously known as the binomial theorem depending on the source. Even more confusingly a number of these (and other) related results are variously known as the binomial formula, binomial expansion.** Binomial theorem** describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power (*x* + *y*)* ^{n}* into a sum involving terms of the form

*ax*, where the exponents

^{b}y^{c}*b*and

*c*are nonnegative integers with

*b*+

*c*=

*n*, and the coefficient

*a*of each term is a specific positive integer depending on

*n*and

*b*. When an exponent is zero, the corresponding power is usually omitted from the term.