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Selforganizology, 2022, 9(1-2): 17-34
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Article

Inauguration of Kifilideen theorem of matrix transformation of negative power of - n of trinomial expression in which three variables x, y and z are found in parts of the trinomial expression with some other applications

Kifilideen L. Osanyinpeju
Agricultural and Bio-Resources Engineering Department, College of Engineering, Federal University of Agriculture Abeokuta, Ogun State, Nigeria

Received 27 November 2021;Accepted 21 December 2021;Published 1 June 2022
IAEES

Abstract
Kifilideen trinomial theorem of negative power of - n is theorem which is used to generate the series and terms of a trinomial expression of negative power of - n in an orderly and periodicity manner that is based on standardized and matrix methods. Negative power of Newton binomial theorem had been used to produce series of partial fractions of a compound fraction. The establishment of the negative power of - n of trinomial theorem would extend the number of compound fraction in which series (expansion) can be produced. This study applied Kifilideen expansion of negative power of - n of Kifilideen trinomial theorem for the transformation of compound fraction into series of partial fractions with other developments. A theorem of matrix transformation of negative power of - n of trinomial expression in which three variables x, y and z are found in parts of the trinomial expression was inauguration. The development would ease the process of evaluating such trinomial expression of negative power of - n. This standardized and matrix method used in arranging the terms of the Kifilideen expansion of negative power of - n of trinomial expression yield an interesting results in which it is utilized in transforming compound fraction into series of partial fractions in a unique way.

Keywords compound fraction;series;partial fraction;combination;kif matrix;Kifilideen standardized method.



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