1. Stating the problem: Fully simplify both expressions separately, then add or multiply as required.\n\n2. Simplify the radicals part: \n\n\tFor $3\sqrt{75} + \sqrt{45} + 2\sqrt{20}$\n\t- $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$\n\t- $\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}$\n\t- $\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$\n\n3. Substitute back: \n\t$3\sqrt{75} + \sqrt{45} + 2\sqrt{20} = 3 \times 5\sqrt{3} + 3\sqrt{5} + 2 \times 2\sqrt{5} = 15\sqrt{3} + 3\sqrt{5} + 4\sqrt{5}$\n\n4. Combine like terms: \n\t$3\sqrt{5} + 4\sqrt{5} = 7\sqrt{5}$\n\n5. So, simplified radicals expression: \n\t$15\sqrt{3} + 7\sqrt{5}$\n\n6. Now expand and simplify $(2 + \sqrt{5})(8 - \sqrt{5})$: \n\tUse distributive property (FOIL):\n\t$= 2 \times 8 - 2 \times \sqrt{5} + \sqrt{5} \times 8 - \sqrt{5} \times \sqrt{5}$\n\t$= 16 - 2\sqrt{5} + 8\sqrt{5} - 5$ (since $\sqrt{5} \times \sqrt{5} = 5$)\n\t$= (16 - 5) + (-2\sqrt{5} + 8\sqrt{5})$\n\t$= 11 + 6\sqrt{5}$\n\n7. Final simplified expressions are: \n\tRadicals sum: $15\sqrt{3} + 7\sqrt{5}$\n\tProduct: $11 + 6\sqrt{5}$