Patterns in Trinomial Expansion

Abstract

INTRODUCTION

The main objective of this study is to determine the characteristics of trinomial expansion. Specifically, this study aims to answer the following: The number of terms, numerical coefficient of the nth term, sum of the numerical coefficients, sum of the exponents and the pattern of the trinomial expansion without fixed values, known as variables.

METHODS

The methodology used is basic research, and the patterns were observed before the formula was developed. Some mathematical concepts were used. The first result that was observed was the number of terms of the trinomial expansion. Several terms were developed using arithmetic sequence and combinations. The next step was the patterns of trinomial expansion, the pattern is similar in Pascal's triangle. In finding the specific term it used the repeated permutation. In finding the sum of the coefficient of the trinomial expansion the geometric sequence was used. The sum of the exponent was determined by using quadratic functions and combinations. The pattern in the trinomial expansion is similar to Pascal's triangle with the aid of triangular numbers.

RESULTS

The results were obtained using some mathematical concepts such as: arithmetic sequence, mathematical induction, combinations and ratios.

DISCUSSIONS

The results of this study will facilitate the trinomial expansion with greater ease and speed. It will also help both the teachers and learners in facilitating learning.