To simplify the expression $-4w - 9(-4w + 9)$, follow these steps:

1. Distribute the $-9$ across the terms inside the parentheses: $-4w - 9(-4w + 9) = -4w + 36w - 81$
2. Combine like terms: $-4w + 36w - 81 = 32w - 81$

So, the simplified expression is: $32w - 81$

Would you like more details, or do you have any questions about these steps?

Here are 5 related questions to explore this concept further:

1. How do you solve an equation when both sides have parentheses?
2. What happens when distributing a positive versus a negative number?
3. Can you simplify the expression $5x - 2(3x + 4)$?
4. How would you solve an equation that looks like $2w - 5(w + 3) = 0$?
5. What is the general rule for combining like terms?

Tip: Always watch out for the signs (positive or negative) when distributing across terms in parentheses!