The given expression is $25x^2 - 16$.

This is a difference of squares, which follows the pattern:

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

Here, we can rewrite $25x^2$ as $(5x)^2$ and $16$ as $4^2$. Therefore, the expression becomes:

$25x^2 - 16 = (5x)^2 - 4^2$

Now apply the difference of squares formula:

$25x^2 - 16 = (5x - 4)(5x + 4)$

Thus, the completely factored form of $25x^2 - 16$ is:

$(5x - 4)(5x + 4)$

Would you like more details on any part of this solution?

Here are 5 related questions to extend this concept:

1. How would you factor the expression $9x^2 - 25$?
2. Can every quadratic expression be factored using the difference of squares method?
3. What is the factored form of $4x^2 - 49$?
4. How do you determine if an expression is a difference of squares?
5. What happens when you try to factor $x^2 + 4$, which is a sum of squares?

Tip: Always check for the greatest common factor (GCF) before applying other factoring methods!