binomial

binomial (bī'nō`mēəl), polynomial expression (see polynomial) containing two terms, for example, x+y. The binomial theorem, or binomial formula, gives the expansion of the nth power of a binomial (x+y) for n=1, 2, 3, … , as follows: where the ellipsis (…) indicates a continuation of terms following the same pattern. For example, using the formula and reducing fractions, one obtains (x+y)⁵=x⁵+5x⁴y+10x³y²+10x²y³+5xy⁴+y⁵. The coefficients 1, n, n (n−1)/1·2, etc., of x and y may also be found from an array known as Pascal's triangle (for Blaise Pascal), formed by adding adjacent numbers to find the number below them as follows: