https://file.aiquickdraw.com/mathbot/file/1726724297280mmktvffx.jpg

The given expression is:

\[
-9(-6p^2 + (-8)) + (-9)(-2 - 8p)
\]

Let's simplify this step by step.

### Step 1: Distribute the \(-9\) to the terms inside both parentheses

1. For the first term \(-9(-6p^2 + (-8))\):
   \[
   -9 \times -6p^2 = 54p^2
   \]
   \[
   -9 \times -8 = 72
   \]
   So, the first term simplifies to:
   \[
   54p^2 + 72
   \]

2. For the second term \(-9(-2 - 8p)\):
   \[
   -9 \times -2 = 18
   \]
   \[
   -9 \times -8p = 72p
   \]
   So, the second term simplifies to:
   \[
   18 + 72p
   \]

### Step 2: Combine all the terms
Now we combine both results:
\[
54p^2 + 72 + 18 + 72p
\]

### Step 3: Simplify the constant terms
\[
54p^2 + 72p + (72 + 18)
\]
\[
54p^2 + 72p + 90
\]

Thus, the simplified expression is:

\[
54p^2 + 72p + 90
\]

Would you like more details or have any other questions? Here are five related questions:

1. How do you simplify more complex polynomial expressions?
2. What is the distributive property, and why is it important in simplification?
3. Can this expression be factored further? If so, how?
4. What is the difference between like terms and unlike terms in algebra?
5. How would the simplification change if the expression had subtraction or division?

**Tip:** Always combine like terms after distributing, to keep the expression as simple as possible!

Simplify the expression: -9(-6p^2 - 8) + -9(-2 - 8p)

Learn how to simplify algebraic expressions using the distributive property with step-by-step instructions. This example breaks down the process of simplifying -9(-6p^2 - 8) + -9(-2 - 8p) using basic algebraic rules.

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