# The number of dissimilar terms in the expansion of $(x_1+x_2+.....x_n)^3$ is ?

$\begin{array}{1 1}n^3 \\\large\frac{n^3+3n^2}{4} \\ \large\frac{n(n+1)(n+2)}{6} \\ \large\frac{n^2(n+1)^2}{4}\end{array}$

Toolbox:
• The no. of terms in the expansion of $(x_1+x_2+x_3+....x_r)^n$ is $^{n+r-1}C_{r-1}$
The no. of terms in the expansion of $(x_1+x_2+x_3+....x_r)^n$ is $^{n+r-1}C_{r-1}$
$\therefore$ No. of terms in the expansion of $(x_1+x_2+x_3+....x_n)^3$ is
$^{3+n-1}C_{n-1}=^{2+n}C_{n-1}=\large\frac{(2+n)!}{(n-1)!.3!}$
$=\large\frac{(n+2)(n+1)n}{6}$