To expand the expression $-4(-x - 8)$, distribute $-4$ to each term inside the parentheses.

Here’s how you do it:

$-4(-x - 8)$

1. Distribute $-4$ to $-x$:

$-4 \times (-x) = 4x$

2. Distribute $-4$ to $-8$:

$-4 \times (-8) = 32$

Putting these together:

$-4(-x - 8) = 4x + 32$

So, the expanded expression is $4x + 32$.

Would you like further details or have any questions? Here are some related questions to consider:

1. What happens if you distribute a positive number instead of a negative one?
2. How can expanding expressions help solve equations?
3. What does distributing mean in the context of algebra?
4. Can you combine like terms after expanding an expression?
5. How would you factor the expression $4x + 32$ back to its original form?

Tip: When expanding expressions, always pay attention to the signs (positive or negative) of the terms involved, as they significantly affect the outcome.