APPLICATION OF EXPANSION OF NEGATIVE POWER OF OF KIFILIDEEN TRINOMIAL THEOREM FOR THE TRANSFORMATION OF COMPOUND FRACTION INTO SERIES OF PARTIAL FRACTIONS WITH OTHER DEVELOPMENTS

Kifilideen trinomial theorem of negative power of is theorem which is used to generate the series and terms of a trinomial expression of negative power of 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 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 of Kifilideen trinomial theorem for the transformation of compound fraction into series of partial fractions with other developments. Kifilideen theorem of matrix transformation of negative power of of trinomial expression in which three variables are found in parts of the trinomial expression was developed. The development would ease the process of evaluating such trinomial expression of negative power of . This standardized and matrix method used in arranging the terms of the Kifilideen expansion of negative power of 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.