Выполните умножение 5, 6, 8, 9

5. Выполните умножение: а) $$\frac{2}{5}x^2 \cdot 5y^3 = 2x^2y^3$$ б) $$-3a \cdot \frac{2}{a} = -6$$ в) $$\frac{3}{4}a \cdot \left(-\frac{2}{3}y\right) = -\frac{1}{2}ay$$ г) $$\sqrt{8x} \cdot \sqrt{2y^2x} = \sqrt{16x^2y^2} = 4|xy|$$ д) $$0,1(5)x^2y \cdot \left(-\frac{3}{10}\right)xy^2 = \frac{1}{6}x^2y \cdot \left(-\frac{3}{10}\right)xy^2 = -\frac{1}{20}x^3y^3$$ 6. Выполните деление: а) $$21x^3y^2 : (3xy) = 7x^2y$$ б) $$-18x^3y^2 : (-6xy^2) = 3x^2$$ в) $$\frac{3}{5}a^6b^2x : \left(\frac{1}{5}a^4bx\right) = 3a^2b$$ г) $$35a^4b^5 : (7a^2b^3) = 5a^2b^2$$ 8. Вычислите: а) $$(\sqrt{8} + \sqrt{32})\sqrt{2} = (2\sqrt{2} + 4\sqrt{2})\sqrt{2} = 6\sqrt{2} \cdot \sqrt{2} = 6 \cdot 2 = 12$$ б) $$(\sqrt{27} - \sqrt{12})\sqrt{3} = (3\sqrt{3} - 2\sqrt{3})\sqrt{3} = \sqrt{3} \cdot \sqrt{3} = 3$$ в) $$2\sqrt{5}( \sqrt{125} - 3\sqrt{5}) = 2\sqrt{5}(5\sqrt{5} - 3\sqrt{5}) = 2\sqrt{5}(2\sqrt{5}) = 4 \cdot 5 = 20$$ г) $$(4\sqrt{24} + 2\sqrt{54})(-0,5\sqrt{6}) = (4 \cdot 2\sqrt{6} + 2 \cdot 3\sqrt{6})(-0,5\sqrt{6}) = (8\sqrt{6} + 6\sqrt{6})(-0,5\sqrt{6}) = 14\sqrt{6}(-0,5\sqrt{6}) = 14 \cdot (-0,5) \cdot 6 = -7 \cdot 6 = -42$$ 9. Раскройте скобки: а) $$(\sqrt{3} + 7)(\sqrt{3} - 7) = (\sqrt{3})^2 - 7^2 = 3 - 49 = -46$$ б) $$(2\sqrt{2} + 1)(3\sqrt{2} - 4) = 2\sqrt{2} \cdot 3\sqrt{2} - 2\sqrt{2} \cdot 4 + 1 \cdot 3\sqrt{2} - 1 \cdot 4 = 6 \cdot 2 - 8\sqrt{2} + 3\sqrt{2} - 4 = 12 - 5\sqrt{2} - 4 = 8 - 5\sqrt{2}$$ в) $$(\sqrt{12} - 5)(2\sqrt{5} + 12) = (2\sqrt{3} - 5)(2\sqrt{5} + 12) = 4\sqrt{15} + 24\sqrt{3} - 10\sqrt{5} - 60$$ г) $$(5\sqrt{7} - \sqrt{13})(\sqrt{13} + 5\sqrt{7}) = (5\sqrt{7} - \sqrt{13})(5\sqrt{7} + \sqrt{13}) = (5\sqrt{7})^2 - (\sqrt{13})^2 = 25 \cdot 7 - 13 = 175 - 13 = 162$$