The given expression is:

\[
4x^2 - 81y^2
\]

This is a difference of squares. The difference of squares formula is:

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

We can rewrite the expression in the form of \(a^2 - b^2\) by identifying \(a\) and \(b\):

\[
4x^2 = (2x)^2 \quad \text{and} \quad 81y^2 = (9y)^2
\]

So, the expression becomes:

\[
(2x)^2 - (9y)^2
\]

Applying the difference of squares formula:

\[
4x^2 - 81y^2 = (2x - 9y)(2x + 9y)
\]

### Final Answer:
\[
4x^2 - 81y^2 = (2x - 9y)(2x + 9y)
\]

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

Here are 5 related questions to expand your understanding:

1. What is the difference of squares, and why does it work in this case?
2. Can you apply the difference of squares to the expression \(x^4 - 16\)?
3. How would you factor \(9x^2 - 4y^2\) using the difference of squares?
4. What are some examples where the difference of squares is not applicable?
5. How can the factored form of an expression help in solving equations?

**Tip:** Remember that the difference of squares only works when there is subtraction between two perfect squares.

Understand how to factor the expression 4x² - 81y² using the difference of squares formula. This problem involves algebraic manipulation and is suitable for high school students. Learn the step-by-step process with detailed explanations.

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