binomial(redirected from Binomials)
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binomial(bī'nō`mēəl), polynomial expression (see polynomialpolynomial,
mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a1x
..... Click the link for more information. ) 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 PascalPascal, Blaise
, 1623–62, French scientist and religious philosopher. Studying under the direction of his father, a civil servant, Pascal showed great precocity, especially in mathematics and science.
..... Click the link for more information. ), formed by adding adjacent numbers to find the number below them as follows:
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A polynomial with only two terms.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
1. a mathematical expression consisting of two terms, such as 3x + 2y
2. a two-part taxonomic name for an animal or plant
3. referring to two names or terms
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