Let's simplify the given expression step by step:

The expression is:

$2(a - b) - 3(b - a) - 4(a - b)$

Step 1: Expand the terms.

Start by distributing the constants:

$= 2(a - b) - 3(b - a) - 4(a - b)$

$= 2a - 2b - 3(b - a) - 4a + 4b$

Since $b - a = -(a - b)$, we can rewrite $- 3(b - a)$ as $+ 3(a - b)$:

$= 2a - 2b + 3(a - b) - 4a + 4b$

Step 2: Distribute and simplify like terms.

Now expand the $3(a - b)$:

$= 2a - 2b + 3a - 3b - 4a + 4b$

Step 3: Combine like terms.

Now combine all the $a$ terms and the $b$ terms:

$= (2a + 3a - 4a) + (-2b - 3b + 4b)$

$= 1a - 1b$

Thus, the simplified expression is:

$a - b$

Let me know if you want further explanation!

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Here are 5 related questions to explore further:

1. How would you simplify $3(a-b) - 2(b-a) + 5(a-b)$?
2. What happens if you switch all the $a$'s and $b$'s in the expression?
3. Can this simplification change if there are other variables involved?
4. How do you handle negative signs when simplifying similar expressions?
5. What if the expression was $2(a - b)^2 - 3(b - a) + 4(a - b)$?

Tip: Always check if factors like $(a - b)$ can be factored out, as this often simplifies expressions faster!