The given expression is $(3 - \sqrt{5})(3 + \sqrt{5})$.

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

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

Here, $a = 3$ and $b = \sqrt{5}$. Applying the formula:

$(3 - \sqrt{5})(3 + \sqrt{5}) = 3^2 - (\sqrt{5})^2$

Now, simplify:

$3^2 = 9 \quad \text{and} \quad (\sqrt{5})^2 = 5$

Thus:

$9 - 5 = 4$

So, the simplest form of the expression is:

$\boxed{4}$

Would you like more details or further explanation?

Here are some related questions:

1. How does the difference of squares formula work?
2. What is the general process for simplifying radical expressions?
3. Can we apply the difference of squares for other complex numbers?
4. How do we simplify expressions involving square roots?
5. What are some examples where the difference of squares appears in geometry?

Tip: Remember, the difference of squares formula is useful for simplifying expressions with conjugates like $(a - b)(a + b)$.