Development of Kifilideen Trinomial Theorem Using Matrix Approach

Abstract

Overtime the arrangement of the terms of the trinomial expansion of power of n has been an issue in the area of orderliness and periodicity which as make it difficult to assign each element of the expansion in a standardize term. The study developed Kifilideen trinomial theorem using matrix approach. The Kifilideen equations to determine the power combination of any term of kif trinomial expansion and position of any term in the series of the expansion in a group or column of a kif matrix were inaugurated. The kif row column matrix formula was also established for any kif expansion of trinomial expression of power n. The kif equation that ascertain the power combination of any term is given as CP = ?90t + 81a + 90m + n90 while the position of a term in group or column of kif matrix is derived using Rm = ? 90rn+90 + Fm. The kif row column matrix formula is stated as CPrc = ?90 r + 81 c + n09. The novel approach would enable all the terms of the expansion of trinomial expression of power of n to be generated with easy and allow accurate prediction of the trinomial coefficients and any term produce in the trinomial expansion of a very large power of n to be obtainable without any difficulty