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To find the factors of \( x^2 - 81 \), we can use the difference of squares formula, which states:

\[
a^2 - b^2 = (a + b)(a - b)
\]

In this case:

1. Recognize that \( x^2 - 81 \) is a difference of squares where:
   - \( a = x \)
   - \( b = 9 \) (since \( 81 = 9^2 \))

2. Apply the difference of squares formula:
   \[
   x^2 - 81 = (x + 9)(x - 9)
   \]

Thus, the correct factorization of \( x^2 - 81 \) is \((x + 9)(x - 9)\).

### Answer:
The correct option is:
- **(x + 9)(x - 9)**

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

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### Related Questions:
1. What is the difference of squares formula and when can it be used?
2. How do you factor expressions like \( x^2 - 49 \)?
3. What are the steps to verify that \((x + 9)(x - 9)\) expands to \( x^2 - 81 \)?
4. Why is the expression \( x^2 - 81 \) not considered a prime polynomial?
5. Can the difference of squares formula be used if the expression is \( x^2 + 81 \)?

### Tip:
Always check if an expression is a difference of squares when you see a subtraction involving perfect squares!

Learn how to factor the expression x^2 - 81 by applying the difference of squares formula. This problem covers key algebraic concepts in factoring and is suitable for students in Grade 9.

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