<ol>
<li>1) $$7\sqrt{2} - 3\sqrt{8} + 4\sqrt{18} = 7\sqrt{2} - 3\sqrt{4\cdot 2} + 4\sqrt{9\cdot 2} = 7\sqrt{2} - 3 \cdot 2\sqrt{2} + 4 \cdot 3\sqrt{2} = 7\sqrt{2} - 6\sqrt{2} + 12\sqrt{2} = 13\sqrt{2}$$</li>
<li>2) $$(\sqrt{90} - \sqrt{40}) \cdot \sqrt{10} = (\sqrt{9 \cdot 10} - \sqrt{4 \cdot 10}) \cdot \sqrt{10} = (3\sqrt{10} - 2\sqrt{10}) \cdot \sqrt{10} = \sqrt{10} \cdot \sqrt{10} = 10$$</li>
<li>3) $$(3\sqrt{5} - 2)^2 = (3\sqrt{5})^2 - 2 \cdot 3\sqrt{5} \cdot 2 + 2^2 = 9 \cdot 5 - 12\sqrt{5} + 4 = 45 - 12\sqrt{5} + 4 = 49 - 12\sqrt{5}$$</li>
<li>4) $$(2\sqrt{3} + 3\sqrt{5})(2\sqrt{3} - 3\sqrt{5}) = (2\sqrt{3})^2 - (3\sqrt{5})^2 = 4 \cdot 3 - 9 \cdot 5 = 12 - 45 = -33$$</li>
</ol>
<strong>Ответ:</strong><br>
1) $$13\sqrt{2}$$<br>
2) 10<br>
3) $$49 - 12\sqrt{5}$$<br>
4) -33