How can I express the multinomial theorem by sum and production for $(a+b+c)$?

How can I express the multinomial theorem by sum and production for
$(a+b+c)$?

How can I express the multinomial theorem for $(a+b+c)$?
$$\begin{align*}\left(x_1+x_2+x_3\right)^2=\sum _{k_1+k_2+k_3=2}
\left(\begin{array}{c} 2 \\ k_1,k_2,k_3 \end{array}\right)\prod _{1\leq
t\leq n} x_t^{k_t}\end{align*}$$
How about the case: $(a+b+c)^2$?