6) 3√2(5√2-√32); в) (4-5√2)2; г) (√7-√3)(√7+2√3).

6. Упростите выражения:

1. 6)

   \(3\sqrt{2}(5\sqrt{2}-\sqrt{32})\) = \(3\sqrt{2}(5\sqrt{2}-4\sqrt{2})\) = \(3\sqrt{2} \cdot \sqrt{2}\) = \(3 \cdot 2 = 6\)

2. в)

   \((4-5\sqrt{2})^2\) = \(4^2 - 2 \cdot 4 \cdot 5\sqrt{2} + (5\sqrt{2})^2\) = \(16 - 40\sqrt{2} + 50\) = \(66 - 40\sqrt{2}\)

3. г)

   \((\sqrt{7}-\sqrt{3})(\sqrt{7}+2\sqrt{3})\) = \((\sqrt{7})^2 + 2\sqrt{3}\sqrt{7} - \sqrt{3}\sqrt{7} - \sqrt{3} \cdot 2\sqrt{3}\) = \(7 + 2\sqrt{21} - \sqrt{21} - 6\) = \(1 + \sqrt{21}\)

Ответ: 6) 6; в) 66 - 40√2; г) 1 + √21.