Find the coefficient of `x^(40)` in the expansion of `(1+2x+x^2)^(27)dot`

Explanation

To find the coefficient of \( x^{40} \) in the expansion of \( (1 + 2x + x^2)^{27} \), we can follow these steps:

### Step 1: Rewrite the Expression
We start with the expression \( (1 + 2x + x^2)^{27} \). This expression has three terms, which makes it unsuitable for direct application of the binomial theorem. However, we can treat it as a polynomial and find the required coefficient.

### Step 2: Identify the General Term
The general term in the expansion of \( (1 + 2x + x^2)^{27} \) can be expressed using the multinomial expansion. The general term can be written as:
\[
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