Multiply and simplify. \( \begin{array}{l}(\sqrt{x}-\sqrt{2})(\sqrt{x}+\sqrt{2})=x-2 \\ (5 \sqrt{x}-\sqrt{2})^{2}=\text { II }\end{array} \)
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The expression \( (\sqrt{x}-\sqrt{2})(\sqrt{x}+\sqrt{2}) \) can be simplified using the difference of squares formula, which gives us \( x - 2 \). This provides a clear and concise result: \( x - 2 \). For the second expression \( (5\sqrt{x}-\sqrt{2})^2 \), we can apply the square of a binomial formula \( (a-b)^2 = a^2 - 2ab + b^2 \). Setting \( a = 5\sqrt{x} \) and \( b = \sqrt{2} \), we find: \[ (5\sqrt{x})^2 - 2 \cdot 5\sqrt{x} \cdot \sqrt{2} + (\sqrt{2})^2 = 25x - 10\sqrt{2}\sqrt{x} + 2 = 25x - 10\sqrt{2x} + 2. \] Thus, the final simplified expression for II is \( 25x - 10\sqrt{2x} + 2 \).