Find the coefficient of `a^4`in the product `(1+2a)^4(2-a)^5`using binomial theorem.

Explanation

To find the coefficient of \( a^4 \) in the product \( (1 + 2a)^4 (2 - a)^5 \), we will use the Binomial Theorem to expand both expressions separately and then find the relevant terms that contribute to \( a^4 \).

### Step 1: Expand \( (1 + 2a)^4 \)

Using the Binomial Theorem, the expansion of \( (x + y)^n \) is given by:

\[
\sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k
...