Question

The constant term in the expansion of $\left(2 x+\frac{1}{x^7}+3 x^2\right)^5$ is_____

Answer 1

General term is $\sum \frac{5 !(2 x)^{n_1}\left(x^{-7}\right)^{n_2}\left(3 x^2\right)^{n_3}}{n_{1} ! n_{2} ! n_{3} !}$
For constant term,
$n _1+2 n _3=7 n _2$
$\& n _1+ n _2+ n _3=5$
Only possibility $n _1=1, n _2=1, n _3=3$
$\Rightarrow$ constant term $=1080$