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 x 2 + 2 x y + y 2 . 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 .