How is the expression (a + √b)(a - √b) simplified?

The expression ((a + \sqrt{b})(a - \sqrt{b})) can be simplified using the difference of squares formula, which states that ((x + y)(x - y) = x^2 - y^2). Here, (x) is (a) and (y) is (\sqrt{b}).

When applying this formula, we substitute (x) and (y) into the formula:

1. Calculate (x^2):

   • This is (a^2) since (x = a).

2. Calculate (y^2):

   • This is ((\sqrt{b})^2), which simplifies to (b).

After performing the calculations, the expression simplifies to:

[ a^2 - b ]

This matches the first choice provided. The other choices do not represent the correct application of the difference of squares. For example, (a^2 + b) adds the squares instead of subtracting them, while the others introduce unnecessary terms or incorrect combinations of (a) and (b). Therefore, ((a + \sqrt{b})(a