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-by-step Solution:

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
...