What is the result of (a + √b)(a - √b)?

To solve the expression ((a + \sqrt{b})(a - \sqrt{b})), you can recognize that this is a classic case of the difference of squares formula. The difference of squares states that ((x + y)(x - y) = x^2 - y^2), where (x) and (y) are any two expressions.

In your case, let (x = a) and (y = \sqrt{b}). Applying the formula, you have:

[

(a + \sqrt{b})(a - \sqrt{b}) = a^2 - (\sqrt{b})^2

]

Now, since ((\sqrt{b})^2) is simply (b), you can substitute this back into the equation:

[

a^2 - b

]

This simplification clearly shows that the result of ((a + \sqrt{b})(a - \sqrt{b})) is indeed (a^2 - b). Therefore, the correct answer is that the expression simplifies to (a^2 - b). This aligns with the answer provided.