The expression given is:

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

This is a **difference of squares**, which can be factored as:

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

Here, \( a^2 = 4y^2 \) and \( b^2 = 81x^4 \).

So, let's rewrite them:

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

Now applying 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 more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you factor other types of polynomials, such as trinomials?
2. What is the general formula for the difference of squares?
3. Can you identify examples where a difference of squares appears in real-world problems?
4. How do you verify the result of factoring by expanding the factors?
5. How can you solve equations involving factored polynomials?

**Tip:** Always check if an expression can be factored using special formulas like the difference of squares to simplify solving.

Learn how to factor the expression 4y^2 - 81x^4 using the difference of squares method. This step-by-step solution covers key algebraic concepts and formulas. Suitable for students in Grades 9-11.

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