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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
Note again that as p + q = 1, the binomial expansion of (p + q) 2 = p 2 + 2pq + q 2 = 1 gives the same relationships. Summing the elements of the Punnett square or the binomial expansion, we obtain the expected genotype proportions among the offspring after a single generation:
The binomial approximation for the square root, + + /, can be applied for the following expression, + where and are real but .. The mathematical form for the binomial approximation can be recovered by factoring out the large term and recalling that a square root is the same as a power of one half.
Binomial (polynomial), a polynomial with two terms; Binomial coefficient, numbers appearing in the expansions of powers of binomials; Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition; Binomial theorem, a theorem about powers of binomials; Binomial type, a property of sequences of polynomials; Binomial series, a ...
The binomial coefficients can be arranged to form Pascal's triangle, in which each entry is the sum of the two immediately above. Visualisation of binomial expansion up to the 4th power. In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem.
In consequence of this definition the binomial theorem can be stated by saying that the sequence {: =,,, …} is of binomial type.; The sequence of "lower factorials" is defined by = () (+). (In the theory of special functions, this same notation denotes upper factorials, but this present usage is universal among combinatorialists.)
A pregnant woman is recovering in the hospital after she was stabbed multiple times by a pizza delivery driver over the size of her tip, according to reports. The incident happened on Sunday, Dec ...
This page was last edited on 31 May 2004, at 15:23 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply ...