The expansion of polynomial expressions raised to a positive integer power is a fundamental topic in algebra and combinatorics. Newton’s Binomial Theorem provides a direct method for expanding expressions containing two variables, . However, no simple general formula is available for expressions involving more than two variables, such as . Consequently, expanding multinomial expressions becomes increasingly complex as the number of variables increases. Therefore, there is a need to develop a generalized mathematical formula that can determine the expansion, coefficients, and total number of terms for any positive integer value of . This research aims to derive such a general formula by analyzing lower-dimensional cases and extending the observed patterns to the general multinomial case