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Binomial theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ⁠ ( x + y ) n {\displaystyle \textstyle (x+y)^{n}} ⁠ expands into a polynomial with terms of the form ⁠ a x k y m {\displaystyle \textstyle ax^{k}y^{m}} ⁠, where the exponents ⁠ k…

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Statement

Examples

Binomial coefficients

Proofs

Generalizations

History

Applications

In abstract algebra

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Binomial theorem

Nodes105
Edges104
Triples90
Avg. degree1.98
Density0.019048
Components1

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Binomial theorem

Top relations

related to history · 20
Binomial theorem → AD, Aryabhata's, BC, Bhāskara II's Līlāvatī, Binomial, By, Diophantus, Euclid, Greek, Halāyudha, Indian, Mahāvīra's Gaṇita-sāra-saṅgraha, Pascal's, Piṅgala, Piṅgala's, Pāṭīgaṇita, Special, The Chandaḥśāstra, The Jain Bhagavati Sutra, Varāhamihira
related to External links · 13
Binomial theorem → Bruce Colletti, Creative Commons Attribution/Share-Alike License, EMS Press, Encyclopedia, Jeff Bryant, Mathematics, Newton, PlanetMath, Solomentsev, Step-by-Step, Stephen Wolfram, This, Wolfram Demonstrations Project
related to Multiple-angle identities · 10
Binomial theorem → According, But De Moivre's, Chebyshev, De Moivre's, For, In, Moivre's, Similarly, There, Using
related to Inductive proof · 9
Binomial theorem → By, For, Induction, Now, On, Pascal's, The, Thus, When
related to Geometric explanation · 7
Binomial theorem → Cavalieri's, Delta, For, If, In, Substituting, With
related to Further generalizations · 5
Binomial theorem → Banach, For, Pochhammer, The, Then
related to Generalized binomial theorem · 5
Binomial theorem → However, In, The, Then, This
related to General Leibniz rule · 4
Binomial theorem → Here, If, Leibniz, The
related to Examples · 3
Binomial theorem → In, Pascal's, The
related to Multi-binomial theorem · 3
Binomial theorem → By, This, When

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displaystyle binomial theorem binom sum formula cdots frac tbinom coefficient coefficients n-k terms term n-1 one two form also century

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SubjectPredicateObjectConfidenceSrc
Binomial theoremrelated to ExamplesThe0.60section
Binomial theoremrelated to ExamplesIn0.60section
Binomial theoremrelated to ExamplesPascal's0.60section
Binomial theoremrelated to External linksSolomentsev0.60section
Binomial theoremrelated to External linksNewton0.60section
Binomial theoremrelated to External linksEncyclopedia0.60section
Binomial theoremrelated to External linksMathematics0.60section
Binomial theoremrelated to External linksEMS Press0.60section
Binomial theoremrelated to External linksStephen Wolfram0.60section
Binomial theoremrelated to External linksStep-by-Step0.60section
Binomial theoremrelated to External linksBruce Colletti0.60section
Binomial theoremrelated to External linksJeff Bryant0.60section

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