| 11. | In " Opus novum de proportionibus " he introduced the binomial coefficients and the binomial theorem.
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| 12. | Shortly after publishing this paper, de Moivre also generalized Newton's noteworthy binomial theorem into the multinomial theorem.
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| 13. | After using the multinomial theorem ( twice the outermost application is the binomial theorem ) and regrouping,
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| 14. | This is a very different branch of mathematics from the Binomial Theorem, again showing his impressive intellectual prowess.
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| 15. | By virtue of the Binomial Theorem.
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| 16. | For larger positive integer values of " n ", the correct result is given by the binomial theorem.
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| 17. | :Alternatively, if you expand ( 1-p ) ^ N with the binomial theorem, the first two terms are 1-Np.
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| 18. | In between, implicit al-Samaw'al, who used it for special cases of the binomial theorem and properties of Pascal's triangle.
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| 19. | Expanding using the binomial theorem and using equation ( 11 ) of the formulas involving binomial coefficients, we obtain
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| 20. | The argument supporting the claim that Khayy�m had a general binomial theorem is based on his ability to extract roots.
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