Решение:

1. a) $$(2\sqrt{3} + 1)(1 - 2\sqrt{3}) = 2\sqrt{3} - 4(\sqrt{3})^2 + 1 - 2\sqrt{3} = 2\sqrt{3} - 4 \times 3 + 1 - 2\sqrt{3} = -12 + 1 = -11$$
2. б) $$(5\sqrt{6} - 6\sqrt{2})^2 = (5\sqrt{6})^2 - 2 \times 5\sqrt{6} \times 6\sqrt{2} + (6\sqrt{2})^2 = 25 \times 6 - 60\sqrt{12} + 36 \times 2 = 150 - 60\sqrt{4 \times 3} + 72 = 222 - 60 \times 2\sqrt{3} = 222 - 120\sqrt{3}$$