The problem presented asks to fully factor the expression $25x^2 - 81$.

This is a difference of squares, which follows the general formula:

$a^2 - b^2 = (a + b)(a - b)$

Here, we can rewrite $25x^2 - 81$ as:

$(5x)^2 - 9^2$

Using the difference of squares formula:

$(5x + 9)(5x - 9)$

Thus, the fully factored form of $25x^2 - 81$ is:

$(5x + 9)(5x - 9)$

The correct answer from the options provided is (5x + 9)(5x - 9).

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How do you identify a difference of squares?
2. What happens if the expression is not a perfect square?
3. Can you apply the difference of squares to trinomials?
4. How do you factor more complex polynomials using other techniques?
5. What is the significance of the difference of squares in solving equations?

Tip: Always look for common factors first before applying the difference of squares method when factoring.