To factor the expression \(16x^{4a} - y^{8a}\), we recognize that it is a difference of squares, which can be factored using the identity:

\[
A^2 - B^2 = (A - B)(A + B)
\]

Here, we can rewrite the expression as:

\[
(4x^{2a})^2 - (y^{4a})^2
\]

Using the difference of squares identity, we get:

\[
16x^{4a} - y^{8a} = (4x^{2a} - y^{4a})(4x^{2a} + y^{4a})
\]

So, the fully factored form of the expression is:

\[
\boxed{(4x^{2a} - y^{4a})(4x^{2a} + y^{4a})}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you factor the expression \(x^4 - y^4\)?
2. What is the difference of squares formula, and how is it applied?
3. How would you factor \(9x^{6} - 25y^{2}\)?
4. Can you explain how to factor \(a^2 - 2ab + b^2\)?
5. What is the process to factor \(x^8 - 1\)?

**Tip:** When factoring expressions, always check if the terms can be rewritten as perfect squares, as it often leads to a difference of squares.

Learn how to factor the expression 16x^4a - y^8a using the difference of squares formula. This problem involves algebraic manipulation and the application of the difference of squares identity, making it suitable for high school students in Grades 9-12.

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