Find the coefficient of `x^7` in the expansion of `(1+3x-2x^3)^(10)dot`

Explanation

To find the coefficient of \( x^7 \) in the expansion of \( (1 + 3x - 2x^3)^{10} \), we can use the multinomial expansion. Let's go through the steps systematically.

### Step 1: Identify the General Term
In the expansion of \( (a + b + c)^n \), the general term \( T \) can be given by:
\[ T = \frac{n!}{\alpha! \beta! \gamma!} a^\alpha b^\beta c^\gamma \]
where \( \alpha + \beta + \gamma = n \).
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