Let's simplify the expression step by step:

Given:
\[
9(-6p - 4) + 3(3p - 5)
\]

1. **Distribute the coefficients:**

   - \( 9(-6p) + 9(-4) = -54p - 36 \)
   - \( 3(3p) + 3(-5) = 9p - 15 \)

2. **Combine the results:**
   \[
   -54p - 36 + 9p - 15
   \]

3. **Combine like terms (terms with \(p\) and constant terms):**
   \[
   (-54p + 9p) + (-36 - 15) = -45p - 51
   \]

The simplified expression is:
\[
-45p - 51
\]

Would you like a detailed explanation of any step or have any questions?

Here are five related questions you could explore:
1. How do you distribute a negative number across terms inside parentheses?
2. What are like terms, and why can they be combined?
3. How do you simplify expressions with multiple variables?
4. How does the distributive property apply in algebraic expressions?
5. Can you factor the simplified expression \(-45p - 51\)?

**Tip:** Always perform operations step by step to avoid mistakes, especially when dealing with negative signs.

Learn to simplify the algebraic expression 9(-6p - 4) + 3(3p - 5) with a step-by-step breakdown. This guide covers essential algebraic concepts like the distributive property and combining like terms. Perfect for students in Grades 8-10.

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