Find the coefficient of `x^5` in the expansioin of the product `(1+2x)^6(1-x)^7dot`

Explanation

To find the coefficient of \( x^5 \) in the expansion of the product \( (1 + 2x)^6 (1 - x)^7 \), we can use the Binomial Theorem.

### Step 1: Expand \( (1 + 2x)^6 \)

Using the Binomial Theorem, we can expand \( (1 + 2x)^6 \):
\[ (1 + 2x)^6 = \sum_{k=0}^{6} \binom{6}{k} (2x)^k = \sum_{k=0}^{6} \binom{6}{k} 2^k x^k \]
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