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The expression to be factored is \(81x^2 - 64\), which is a classic case of the "difference of squares." The difference of squares formula is given by:

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

We can express the given terms as squares:
\[
81x^2 = (9x)^2 \quad \text{and} \quad 64 = 8^2
\]

So, we apply the difference of squares formula:
\[
81x^2 - 64 = (9x + 8)(9x - 8)
\]

Thus, the factored form of \(81x^2 - 64\) is:
\[
(9x + 8)(9x - 8)
\]

This matches option **A** in the provided choices.

Would you like more details on this, or do you have any other questions?

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Here are 5 related questions you could explore:
1. How would you factor an expression like \(49x^2 - 25\)?
2. Can you apply the difference of squares formula to higher powers, like \(x^4 - 16\)?
3. What happens when an expression looks like a difference of squares but isn't, e.g., \(x^2 + 4\)?
4. How does the difference of squares formula relate to completing the square?
5. How can you quickly recognize if a quadratic expression can be factored using the difference of squares?

**Tip:** Always check if the terms are perfect squares when asked to factor a binomial that involves subtraction—it often indicates a difference of squares!

Factor the difference of two squares: 81x^2 - 64

Learn how to factor the difference of squares 81x^2 - 64 using the formula a^2 - b^2 = (a + b)(a - b). This problem is suitable for students in Grades 9-10 and provides a clear example of the difference of squares theorem.

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