Question #N696
The expression $(\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y})$ is equivalent to which of the following?
A. $\sqrt{x^2 - y^2}$
B. $x^2 - y^2$
C. $x - y$
D. $\sqrt{x} - \sqrt{y}$
Correct Answer is: C
This expression is in the form of the difference of squares: (a + b)(a - b) = a^2 - b^2. In this case, a = \sqrt{x} and b = \sqrt{y}. Therefore, (\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y}) = (\sqrt{x})^2 - (\sqrt{y})^2 = x - y.