General Certificate of Secondary Education (GCSE) Maths Practice Exam

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.