1.1.2 \( (2-\sqrt{x})(2+\sqrt{x}) \)

The expression can be rewritten using the difference of squares formula, which states that \( (a-b)(a+b) = a^2 - b^2 \). In this case, let \( a = 2 \) and \( b = \sqrt{x} \). When we apply the formula, we get: \[ (2 - \sqrt{x})(2 + \sqrt{x}) = 2^2 - (\sqrt{x})^2 = 4 - x \] So, the simplified form of the expression is \( 4 - x \). This elegant transformation shows how algebraic identities can be quite handy in simplifying expressions! The difference of squares isn't just a neat trick; it's a powerful tool in algebra that helps simplify not only polynomials but also solve equations. For instance, if you encounter a situation where you need to factor a quadratic, recognizing it as a difference of squares can save you time and effort. Just remember: whenever you see something resembling \( (a-b)(a+b) \), dive right in and unlock that difference!