Упрощение выражений

371 a)

$$ (2\sqrt{3}-3\sqrt{2})(2\sqrt{3}+3\sqrt{2}) = (2\sqrt{3})^2 - (3\sqrt{2})^2 = 4 \cdot 3 - 9 \cdot 2 = 12 - 18 = -6 $$

Ответ: $$ -6 $$

371 б)

$$ (\sqrt{32}-3\sqrt{12})(2\sqrt{8}+\sqrt{108}) = (4\sqrt{2} - 3\cdot 2\sqrt{3})(2\cdot 2\sqrt{2} + 6\sqrt{3}) = (4\sqrt{2}-6\sqrt{3})(4\sqrt{2}+6\sqrt{3}) = (4\sqrt{2})^2 - (6\sqrt{3})^2 = 16\cdot 2 - 36 \cdot 3 = 32 - 108 = -76 $$

Ответ: $$ -76 $$

371 в)

$$ (3\sqrt{5}-2\sqrt{6})^2 = (3\sqrt{5})^2 - 2 \cdot 3\sqrt{5} \cdot 2\sqrt{6} + (2\sqrt{6})^2 = 9 \cdot 5 - 12\sqrt{30} + 4 \cdot 6 = 45 - 12\sqrt{30} + 24 = 69 - 12\sqrt{30} $$

Ответ: $$ 69-12\sqrt{30} $$

371 г)

$$ (2-\sqrt{6})^2 - (5+\sqrt{6}) = 4 - 4\sqrt{6} + 6 - 5 - \sqrt{6} = 5 - 5\sqrt{6} $$

Ответ: $$ 5-5\sqrt{6} $$