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.