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!

Learn how to simplify the algebraic expression 2(a-b) - 3(b-a) - 4(a-b) step by step. This problem involves key algebraic concepts like the distributive property and combining like terms. Suitable for students in Grades 8-10.

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