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?

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!