The expression given in the image is $81x^2 - 16$, which needs to be factored.

This expression is a difference of squares, which has the general form:

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

Here:

$81x^2 = (9x)^2 \quad \text{and} \quad 16 = 4^2$

So, we can write the expression as:

$81x^2 - 16 = (9x)^2 - 4^2$

Now applying the difference of squares formula:

$81x^2 - 16 = (9x - 4)(9x + 4)$

Thus, the factored form of the expression is:

$(9x - 4)(9x + 4)$

Would you like more details on this factorization process or have any further questions?

Here are some related questions to expand your understanding:

1. How do you factor a sum of squares, such as $a^2 + b^2$?
2. What are the differences between factoring trinomials and factoring the difference of squares?
3. Can you factor expressions with higher powers, such as $x^4 - 16$?
4. How does the difference of cubes formula differ from the difference of squares?
5. How do you determine when to use the difference of squares method versus other factoring techniques?

Tip: Always look for common factors in all terms before applying special factorization formulas.