Let's simplify the expression \( 6(2a - b) - 5(b - 2a) \).

### Step 1: Distribute the constants.
- Distribute \(6\) to both \(2a\) and \(-b\):
\[
6(2a - b) = 12a - 6b
\]
- Distribute \(-5\) to both \(b\) and \(-2a\):
\[
-5(b - 2a) = -5b + 10a
\]

### Step 2: Combine like terms.
Now, the expression becomes:
\[
12a - 6b - 5b + 10a
\]
Combine the terms involving \(a\) and the terms involving \(b\):
\[
(12a + 10a) + (-6b - 5b) = 22a - 11b
\]

So, the simplified expression is:
\[
22a - 11b
\]

Would you like further details or have any questions?

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Here are 5 questions related to this problem:

1. How do you distribute a constant over terms inside parentheses?
2. What are like terms in an algebraic expression?
3. How do you combine like terms involving variables?
4. Can you factor the simplified expression \(22a - 11b\)?
5. How would this process change if the signs in the parentheses were reversed?

**Tip:** Always look for like terms after distributing constants to simplify your expressions.

Learn how to simplify the algebraic expression 6(2a - b) - 5(b - 2a) using the distributive property and combining like terms. This step-by-step solution is suitable for students in Grades 7-9 and covers key algebraic concepts.

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