The expression $25x^2 - 81$ can be factored using the difference of squares method.

Step 1: Recognize the difference of squares

The given expression is $25x^2 - 81$. This fits the pattern of a difference of squares:

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

Here, $a = 5x$ and $b = 9$, because:

$25x^2 = (5x)^2 \quad \text{and} \quad 81 = 9^2$

Step 2: Apply the difference of squares formula

Using the difference of squares formula, you can factor the expression as follows:

$25x^2 - 81 = (5x - 9)(5x + 9)$

So, the factored form of $25x^2 - 81$ is $(5x - 9)(5x + 9)$.

Would you like more details or have any questions?

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Here are five related questions:

1. How can you verify that $(5x - 9)(5x + 9)$ is the correct factorization?
2. What other methods can be used to factor quadratic expressions?
3. How would you solve the equation $25x^2 - 81 = 0$ after factoring it?
4. Can the difference of squares method be used for expressions like $x^4 - 16$?
5. How do you expand the product $(5x - 9)(5x + 9)$ back into the original expression?

Tip: Always check your factored expressions by expanding them back to ensure they match the original expression!