4, left parenthesis, minus, p, minus, 3, q, right parenthesis, plus, 9, q, minus, 10, left parenthesis, 6, q, plus, 3, p, right parenthesis4(−p−3q)+9q−10(6q+3p)

To simplify the expression \( 4(-p - 3q) + 9q - 10(6q + 3p) \), we will follow these steps:

1. Distribute the constants into the parentheses.
2. Combine like terms.

**Step 1: Distribute**

1. \( 4(-p - 3q) = -4p - 12q \)
2. \( -10(6q + 3p) = -60q - 30p \)

Now we can rewrite the expression:

\[
-4p - 12q + 9q - 60q - 30p
\]

**Step 2: Combine like terms**

Combine the \( p \) terms:

\[
-4p - 30p = -34p
\]

Combine the \( q \) terms:

\[
-12q + 9q - 60q = -63q
\]

Putting it all together, the simplified expression is:

\[
-34p - 63q
\]

If you have any questions or need further details, feel free to ask!

Here are some related questions you might consider:

1. What are the steps to solve similar expressions with different variables?
2. How can we factor expressions like \( -34p - 63q \)?
3. What would happen if we changed the coefficients in the original expression?
4. Can you explain how to graph a linear equation represented by this expression?
5. How do we handle expressions with more than two variables? 

**Tip:** When simplifying expressions, always pay attention to distributing negative signs correctly to avoid errors.

This page explains how to simplify the expression 4(-p - 3q) + 9q - 10(6q + 3p) using the distributive property and combining like terms. The final result is -34p - 63q, suitable for students in Grades 7-9.

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