Is there a general formula for the following expression?

Question

I am working on a proof, and came to the point where I need a general expression for the formula, taking real numbers $x_i$ and an integer $k$, of :

$(x_1+x_2+...+x_n)^k$

I now I could apply the Newtons Binomial Theorem several times to get this expression. But, do you know what I should get?

Answer 1

You need the Multinomial theorem.