Let's simplify the expression step by step:

$-4(-8w - 4x) - 7x - 10(-10x + 8w)$

Step 1: Distribute the terms inside the parentheses

• For the first term, distribute $-4$ to both $-8w$ and $-4x$: $-4(-8w) = 32w, \quad -4(-4x) = 16x$
• For the second term, distribute $-10$ to both $-10x$ and $8w$: $-10(-10x) = 100x, \quad -10(8w) = -80w$

Now, the expression becomes: $32w + 16x - 7x + 100x - 80w$

Step 2: Combine like terms

• Combine the $w$-terms: $32w - 80w = -48w$
• Combine the $x$-terms: $16x - 7x + 100x = 109x$

Final Expression:

$-48w + 109x$

So, the simplified expression is:

$-48w + 109x$

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

Here are 5 related questions:

1. How do you simplify an expression with multiple variables and terms?
2. What are the rules for distributing negative numbers in parentheses?
3. Can you explain the concept of combining like terms in algebra?
4. How would this process change if there were exponents involved?
5. What happens if you have more than two variables in an expression?

Tip: Always distribute carefully, paying attention to signs (especially negatives), as they are a common source of mistakes.