Answer: Second option.
Step-by-step explanation:
Remember that when you multiply radicals:
[tex](\sqrt[n]{x})(\sqrt[n]{y})=\sqrt[n]{xy}[/tex]
Then, since the radicals have the same index, you can multiply them:
Apply Distributive property:
[tex](\sqrt{3x}+\sqrt{5})(\sqrt{15x}+2\sqrt{30})=\\\\=(\sqrt{3x})(\sqrt{15x})+(\sqrt{3x})(2\sqrt{30})+(\sqrt{5})(\sqrt{15x})+(\sqrt{5})(2\sqrt{30})\\\\=\sqrt{45x^2}+2\sqrt{90x}+\sqrt{75x}+2\sqrt{150}[/tex]
Remember that:
[tex]\sqrt[n]{x^n}=x[/tex]
Then, you can rewrite the expression:
[tex]=\sqrt{3^2*5x^2}+2\sqrt{3^2*5*2x}+\sqrt{5^2*3x}+2\sqrt{5^2*2*3}[/tex]
Simplifying, you get:
[tex]=3x\sqrt{5}+2(3\sqrt{5*2x})+5\sqrt{3x}+2(5\sqrt{2*3})\\\\=3x\sqrt{5}+6\sqrt{10x}+5\sqrt{3x}+10\sqrt{6}[/tex]
