The expression \( 4y^2 - 81x^4 \) is a difference of squares. This can be factored using the identity:

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

Here, \( 4y^2 \) and \( 81x^4 \) can both be written as squares:
- \( 4y^2 = (2y)^2 \)
- \( 81x^4 = (9x^2)^2 \)

Now apply the difference of squares formula:

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

Thus, the factored form of \( 4y^2 - 81x^4 \) is:

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

Would you like further details or explanations on any part of this solution?

Here are 5 related questions to consider:
1. How do you recognize when to use the difference of squares?
2. Can you apply the difference of squares to higher-degree polynomials?
3. What is the general form of the difference of squares, and how does it apply in various problems?
4. How would you factor expressions like \( 16a^4 - 25b^4 \)?
5. Can this factoring method be used in solving equations?

**Tip:** Always check if terms in an expression can be written as perfect squares when factoring differences of squares.

Discover how to factor the expression 4y^2 - 81x^4 using the difference of squares formula. This solution breaks down the steps of recognizing perfect squares and applying the difference of squares identity. Perfect for students in Grades 9-10 learning factoring techniques in algebra.

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