4. Упростите выражение: 1) $$5\sqrt{2} - 4\sqrt{8} + 3\sqrt{32};$$ 2) $$(\sqrt{75} - \sqrt{12})\sqrt{3};$$ 3) $$(\sqrt{7} - 3)^2;$$ 4) $$(\sqrt{5} + 2\sqrt{2})(\sqrt{5} - 2\sqrt{2})$$.

a) $$5\sqrt{2} - 4\sqrt{8} + 3\sqrt{32}$$

$$5\sqrt{2} - 4 \cdot 2\sqrt{2} + 3 \cdot 4\sqrt{2} = 5\sqrt{2} - 8\sqrt{2} + 12\sqrt{2} = 9\sqrt{2}$$

Ответ: $$9\sqrt{2}$$

б) $$(\sqrt{75} - \sqrt{12})\sqrt{3}$$

$$(\sqrt{25 \cdot 3} - \sqrt{4 \cdot 3})\sqrt{3} = (5\sqrt{3} - 2\sqrt{3})\sqrt{3} = 3\sqrt{3} \cdot \sqrt{3} = 3 \cdot 3 = 9$$

Ответ: 9

в) $$(\sqrt{7} - 3)^2$$

$$(\sqrt{7})^2 - 2 \cdot \sqrt{7} \cdot 3 + 3^2 = 7 - 6\sqrt{7} + 9 = 16 - 6\sqrt{7}$$

Ответ: $$16 - 6\sqrt{7}$$

г) $$(\sqrt{5} + 2\sqrt{2})(\sqrt{5} - 2\sqrt{2})$$

$$(\sqrt{5})^2 - (2\sqrt{2})^2 = 5 - 4 \cdot 2 = 5 - 8 = -3$$

Ответ: -3