binomial theorem (redirected from Binomial expansions)

binomial theorem

In algebra, a formula for expansion of the binomial (x + y) raised to any positive integer power. A simple case is the expansion of (x + y)², which is x² + 2xy + y². In general, the expression (x + y)ⁿ expands to the sum of (n + 1)terms in which the power of x decreases from n to 0 while the power of y increases from 0 to n in successive terms. The terms can be represented in factorial notation by the expression [n!/((n − r)!r!)]x^{n − r}y^r in which r takes on integer values from 0 to n.