To factor the expression $16x^4 - y^2$, we can recognize that it is a difference of squares. The difference of squares formula is:

$a^2 - b^2 = (a - b)(a + b)$

Here, $a^2 = 16x^4$ and $b^2 = y^2$.

First, we find the square roots of each term:

$\sqrt{16x^4} = 4x^2 \quad \text{and} \quad \sqrt{y^2} = y$

Now, applying the difference of squares formula:

$16x^4 - y^2 = (4x^2 - y)(4x^2 + y)$

So, the factored form of $16x^4 - y^2$ is:

$(4x^2 - y)(4x^2 + y)$

Would you like more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How would you factor $9x^4 - 25y^2$?
2. Can the expression $16x^4 - y^2$ be factored further?
3. What is the general approach to factoring a difference of squares?
4. How do you recognize a difference of squares in an algebraic expression?
5. What happens if the expression is $16x^4 + y^2$? Can it still be factored?
6. Can you apply the difference of squares formula to $x^2 - 9$?
7. How would you solve the equation $16x^4 - y^2 = 0$ for $x$ and $y$?
8. How does factoring help in solving polynomial equations?

Tip: When factoring, always check first if the expression fits a common pattern like the difference of squares or perfect square trinomials. This can simplify your work significantly.