Rewrite in simplest terms -9(4p-6q)+8q-7(3q-3p)

Let's simplify the expression step by step:

Expression:  
\[
-9(4p - 6q) + 8q - 7(3q - 3p)
\]

### Step 1: Distribute the numbers outside the parentheses.
1. Distribute \(-9\) to both \(4p\) and \(-6q\):
   \[
   -9(4p - 6q) = -36p + 54q
   \]
2. Distribute \(-7\) to both \(3q\) and \(-3p\):
   \[
   -7(3q - 3p) = -21q + 21p
   \]

Now, the expression looks like this:
\[
-36p + 54q + 8q - 21q + 21p
\]

### Step 2: Combine like terms.
- Combine the \(p\) terms: \(-36p + 21p = -15p\)
- Combine the \(q\) terms: \(54q + 8q - 21q = 41q\)

### Final simplified expression:
\[
-15p + 41q
\]

Let me know if you want more details or have any questions.

Here are some related questions:
1. How do you factor expressions like this one?
2. What are like terms in algebraic expressions?
3. How do you distribute negative numbers in parentheses?
4. What is the importance of combining like terms?
5. Can expressions like these be solved for specific values of \(p\) and \(q\)?

**Tip:** When simplifying, always distribute first before combining like terms!

Simplify the algebraic expression -9(4p - 6q) + 8q - 7(3q - 3p) step-by-step. Learn how to distribute terms and combine like terms to arrive at the final expression -15p + 41q. This is a common algebraic problem suitable for students in Grades 7-9.

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