# binomial theorem

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## binomial theorem

n. Mathematics
The theorem that specifies the expansion of any power (a + b)m of a binomial (a + b) as a certain sum of products aibj, such as (a + b)2 = a2 + 2ab + b2.

## binomial theorem

n
(Mathematics) a mathematical theorem that gives the expansion of any binomial raised to a positive integral power, n. It contains n + 1 terms: (x + a)n = xn + nxn1a + [n(n–1)/2] xn2a2 +…+ (nk) xnkak + … + an, where (nk) = n!/(n–k)!k!, the number of combinations of k items selected from n

## bino′mial the′orem

n.
the theorem giving the expansion of a binomial raised to any power.
[1865–70]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 binomial theorem - a theorem giving the expansion of a binomial raised to a given powerstatistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parametersprobability theory, theory of probability - the branch of applied mathematics that deals with probabilitiestheorem - a proposition deducible from basic postulates
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A brief investigation led me quickly down the path of binomial expansions, parametric equations, the concept of nesting, and spinners/scroll bars in an Excel spreadsheet.
Milan Pahor introduces and justifies techniques for finding the largest coefficient of binomial expansions. This article presents a series of proofs which, since binomial coefficients are commonly encountered in the algebra and probability sections of our courses, may be of interest to our students.
Then, students are given four or five notebooks, written on various topics such as patterns on binomial expansions and series approximations.

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