Pascal's triangle is primarily used for binomial coefficients in the expansion of (a+b)^n, but for expressions involving more than two variables, such as (a+b+c)^n or (a+b+c+...+d)^n, multinomial coefficients are required. The multinomial coefficient for m variables raised to the power n is expressed as (i+j+...+k)!/(i! j!...k!). This formula accounts for the different arrangements of the variables in the expansion. Thus, while Pascal's triangle is useful for binomials, multinomial coefficients are necessary for handling multiple variables in polynomial expansions. Understanding this distinction is essential for solving equations involving multiple terms raised to a power.
