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The problem asks to factor the expression \( 16y^4 - 25x^4 \). This expression is a **difference of squares**, which can be factored using the formula:

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

Here, we can rewrite \( 16y^4 \) and \( 25x^4 \) as perfect squares:

\[
16y^4 = (4y^2)^2 \quad \text{and} \quad 25x^4 = (5x^2)^2
\]

Now, applying the difference of squares formula:

\[
16y^4 - 25x^4 = (4y^2 - 5x^2)(4y^2 + 5x^2)
\]

This corresponds to option **B**: \((4y^2 + 5x^2)(4y^2 - 5x^2)\).

Would you like a detailed breakdown of the steps or have any further questions?

Here are 5 related questions to consider:
1. How do you factor a difference of cubes?
2. What is the formula for factoring a perfect square trinomial?
3. Can the expression \(4y^2 - 5x^2\) be factored further?
4. How can you determine if a polynomial is a difference of squares?
5. What is the general strategy for factoring polynomials?

**Tip:** Always check if an expression can be rewritten as a perfect square or cube to simplify factoring.

Factor the following expression: 16y^4 - 25x^4

Learn how to factor the polynomial 16y^4 - 25x^4 by applying the difference of squares formula. This problem illustrates core algebra concepts such as polynomial factoring and the difference of squares theorem. Suitable for students in Grades 9-12.

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