Let's simplify the expression:

\[
-9(-n + 8) - 9(-8n - 2)
\]

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

For the first part, \(-9(-n + 8)\):

\[
-9 \cdot (-n) = 9n
\]
\[
-9 \cdot 8 = -72
\]

So, \(-9(-n + 8) = 9n - 72\).

For the second part, \(-9(-8n - 2)\):

\[
-9 \cdot (-8n) = 72n
\]
\[
-9 \cdot (-2) = 18
\]

So, \(-9(-8n - 2) = 72n + 18\).

### Step 2: Combine the simplified parts:

\[
9n - 72 + 72n + 18
\]

### Step 3: Combine like terms:

\[
(9n + 72n) + (-72 + 18)
\]
\[
81n - 54
\]

### Final Answer:
\[
81n - 54
\]

Would you like further details on this, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you distribute a negative number across parentheses?
2. What is the importance of combining like terms in algebra?
3. How would the result change if one of the signs in the original expression were different?
4. Can this expression be factored further?
5. How would this expression behave if you substituted a value for \(n\)?

**Tip:** Always distribute the signs carefully when simplifying expressions with parentheses!

Learn how to simplify the algebraic expression −9(−n+8)−9(−8n−2) using the distributive property and combining like terms. This problem covers key algebraic concepts such as distribution and simplifying expressions, making it suitable for students in Grades 7-9.

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