binomial

binomial , polynomial expression (see polynomial ) containing two terms, for example, x + y. The binomial theorem, or binomial formula, gives the expansion of the n th 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 +5 x⁴y +10 x³y² +10 x²y³ +5 xy⁴ + 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:

bi·no·mi·al / bīˈnōmēəl/ • n. 1. Math. an algebraic expression of the sum or the difference of two terms. 2. a two-part name, esp. the Latin name of a species of living organism. • adj. 1. Math. consisting of two terms. ∎  of or relating to a binomial or to the binomial theorem. 2. having or using two names, used esp. of the Latin name of a species of living organism.

binomial (math.) having two terms. XVI. f. F. binôme or modL. binōmius, of uncert. orig. (see BI-, -IAL).