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

<p><strong>1)</strong> $$5\sqrt{2} - 4\sqrt{8} + 3\sqrt{32} = 5\sqrt{2} - 4\sqrt{4 \cdot 2} + 3\sqrt{16 \cdot 2} = 5\sqrt{2} - 4 \cdot 2\sqrt{2} + 3 \cdot 4\sqrt{2} = 5\sqrt{2} - 8\sqrt{2} + 12\sqrt{2} = 9\sqrt{2}$$</p> <p><strong>2)</strong> $$(\sqrt{75} - \sqrt{12})\sqrt{3} = (\sqrt{25 \cdot 3} - \sqrt{4 \cdot 3})\sqrt{3} = (5\sqrt{3} - 2\sqrt{3})\sqrt{3} = 3\sqrt{3} \cdot \sqrt{3} = 3 \cdot 3 = 9$$</p> <p><strong>3)</strong> $$(\sqrt{7} - 3)^{2} = (\sqrt{7})^{2} - 2 \cdot \sqrt{7} \cdot 3 + 3^{2} = 7 - 6\sqrt{7} + 9 = 16 - 6\sqrt{7}$$</p> <p><strong>4)</strong> $$(\sqrt{5} + 2\sqrt{2})(\sqrt{5} - 2\sqrt{2}) = (\sqrt{5})^{2} - (2\sqrt{2})^{2} = 5 - 4 \cdot 2 = 5 - 8 = -3$$</p>