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binomial

binomial (bĪˌnōˈmēəl) [key], 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:;e1;none;1;e1;;;block;;;;no;1;139392n;16544n;;;;;eq1;;;left;stack;;;;;CE5where the ellipsis (…) indicates a continuation of terms following the same pattern. For example, using the formula and reducing fractions, one obtains ( x + y )5 = x 5+5 x 4 y +10 x 3 y 2+10 x 2 y 3+5 x y 4+ y 5. 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:;e2;none;1;e2;;;block;;;;no;1;139392n;54414n;;;;;eq2;comptd;;center;stack;;;;;CE5

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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