The expression $(4ab+5c)(4ab-5c)$ is a difference of squares. Using the identity for the difference of squares:

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

Here, $a = 4ab$ and $b = 5c$. Applying the identity:

$(4ab+5c)(4ab-5c) = (4ab)^2 - (5c)^2$

Now, let's simplify each square:

$(4ab)^2 = 16a^2b^2 \quad \text{and} \quad (5c)^2 = 25c^2$

Thus, the result is:

$(4ab+5c)(4ab-5c) = 16a^2b^2 - 25c^2$

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

Here are 5 related questions you might find useful:

1. What is the difference of squares formula, and how is it derived?
2. How do you expand expressions using binomials that are not a difference of squares?
3. What is the significance of factoring in algebraic simplifications?
4. Can the difference of squares method be applied to trinomials or higher-degree polynomials?
5. How do we simplify expressions involving squares of binomials?

Tip: Always look for special identities like the difference of squares to simplify expressions quickly.