Find the coefficient of `x^6y^3`in the expansion of `(x+2y)^9`.

Explanation

To find the coefficient of \( x^6y^3 \) in the expansion of \( (x + 2y)^9 \), we can follow these steps:

### Step 1: Identify the General Term
The general term \( T_{r+1} \) in the binomial expansion of \( (a + b)^n \) is given by:
\[ T_{r+1} = \binom{n}{r} a^{n-r} b^r \]
For our case, \( a = x \), \( b = 2y \), and \( n = 9 \). Thus, the general term becomes:
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