Answer:
[tex]6y^2\sqrt{10}+12\sqrt{5y}[/tex]
Step-by-step explanation:
Use the distributive property and the rules for forming and simplifying square roots.
(√a)(√b) = √(ab)
√(a²b) = a√b
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[tex]3\sqrt{10}\cdot(y^2\sqrt{4}+\sqrt{8y})=(3\sqrt{10})(2y^2) +(3\sqrt{10})(\sqrt{8y})\\\\=6y^2\sqrt{10}+3\sqrt{80y}\\\\=6y^2\sqrt{10}+3\sqrt{(4^2)(5y)}\\\\=\boxed{6y^2\sqrt{10}+12\sqrt{5y}}\qquad\text{matches the first choice}[/tex]
