(x_1 + x_2 + ... + x_k)^n = sum over all (r_1,...,r_k) with sum r_i = n of [n!/(r_1!r_2!...*r_k!)] * x_1^{r_1} * x_2^{r_2} * ... * x_k^{r_k}.

Number of terms: C(n+k-1, k-1). For trinomial (k=3): C(n+2, 2) terms.

The coefficient n!/(r_1!*...*r_k!) is the multinomial coefficient. It counts the number of ways to arrange n objects where r_i are of type i.

Application: Finding coefficient of x^ay^bz^c in (x+y+z)^n = n!/(a!*b!*c!) if a+b+c = n.