| Share


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.

More on binomial from Infoplease:

See more Encyclopedia articles on: Mathematics

Premium Partner Content
HighBeam Research
Documents Images and Maps Reference
(from Newspapers, Magazines, Journals, Newswires, Transcripts and Books)

Research our extensive archive of more than 80 million articles from 6,500 publications.

Additional search results provided by HighBeam Research, LLC. © Copyright 2005. All rights reserved.

24 X 7

Private Tutor

Click Here for Details
24 x 7 Tutor Availability
Unlimited Online Tutoring
1-on-1 Tutoring