Answer: second option.
Step-by-step explanation:
We know that:
[tex]\sqrt[n]{a^n}=a[/tex]
[tex](a^m)(a^n)=a^{(m+n)[/tex]
Then we can simplify the radicals:
[tex]2\sqrt{8x^3}(3\sqrt{10x^4}-x\sqrt{5x^2})=(2\sqrt{2^2*2*x^2*x})(3\sqrt{10x^4}-x\sqrt{5x^2})=\\\\=2*2*x\sqrt{2x}=3x^2\sqrt{10}-x*x\sqrt{5}\\\\=4x\sqrt{2x}(3x^2\sqrt{10}-x^2\sqrt{5})[/tex]
Since:
[tex](a\sqrt[n]{x})*(b\sqrt[n]{y})=ab\sqrt[n]{xy}[/tex]
We can apply Distributive property:
[tex]4x\sqrt{2x}(3x^2\sqrt{10}-x^2\sqrt{5})\\\\12x^3\sqrt{20x}-4x^3\sqrt{10x}[/tex]
Simplifying:
[tex]12x^3*2\sqrt{5x}-4x^3\sqrt{10x}\\\\24x^3\sqrt{5x}-4x^3\sqrt{10x}[/tex]
