Let's simplify the expression step by step.

The given expression is: $-9(4p - 6q) + 8q - 7(3q - 3p)$

Step 1: Distribute the constants

Distribute $-9$ to both terms inside the parentheses: $-9(4p - 6q) = -9 \cdot 4p + (-9) \cdot (-6q) = -36p + 54q$

Distribute $-7$ to both terms inside the second parentheses: $-7(3q - 3p) = -7 \cdot 3q + (-7) \cdot (-3p) = -21q + 21p$

So, the expression becomes: $-36p + 54q + 8q - 21q + 21p$

Step 2: Combine like terms

Now, combine the terms with $p$ and the terms with $q$:

• Terms with $p$: $-36p + 21p = -15p$
• Terms with $q$: $54q + 8q - 21q = 41q$

Final expression:

$-15p + 41q$

So, the simplified expression is: $-15p + 41q$

Would you like more details on this?

Here are some additional questions to explore:

1. How do you handle distribution when there is a negative sign outside the parentheses?
2. What is the difference between combining like terms and distributing?
3. Can you simplify $7(2p - 5q) + 4p - 3(6p + q)$?
4. Why is it important to group similar variables when simplifying expressions?
5. How do you know which operations to perform first when simplifying?

Tip: Always keep track of signs (positive and negative) when distributing and combining terms to avoid mistakes.