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

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.