1. The problem is to simplify the expression $$(4 - \sqrt{5})(4 + \sqrt{5})$$ and find which of the given options (A. 9, B. 11, C. 21, D. -1) is correct. 2. This expression is a product of conjugates of the form $$(a - b)(a + b)$$, which simplifies using the difference of squares formula: $$ (a - b)(a + b) = a^2 - b^2 $$ 3. Here, $a = 4$ and $b = \sqrt{5}$. 4. Applying the formula: $$ (4 - \sqrt{5})(4 + \sqrt{5}) = 4^2 - (\sqrt{5})^2 $$ 5. Calculate each square: $$ 4^2 = 16 $$ $$ (\sqrt{5})^2 = 5 $$ 6. Substitute back: $$ 16 - 5 = 11 $$ 7. Therefore, the simplified value of the expression is $11$. 8. Comparing with the options, the correct answer is B. 11.