Find the coefficient of `x^7` in the expansion of `(a+3x-2x^3)^(10)dot`

Explanation

To find the coefficient of \(x^7\) in the expansion of \((a + 3x - 2x^3)^{10}\), we will use the multinomial theorem.

### Step-by-step Solution:

1. **Identify the General Term**:
The general term in the expansion of \((a + 3x - 2x^3)^{10}\) can be expressed as:
\[
T = \frac{10!}{n_1! n_2! n_3!} (a)^{n_1} (3x)^{n_2} (-2x^3)^{n_3}
...