Solved: What is the following simplified product? Assume x≥ 0. 2sqrt(8x^3)(3sqrt(10x^4)-xsqrt(5x^2 [Math]

Apply Multiplicative Distribution Law:$$2 \sqrt{8 x^{3}} \times 3 \sqrt{10 x^{4}} - 2 \sqrt{8 x^{3}} \times x \sqrt{5 x^{2}}$$
Multiply the monomials:$$6 \sqrt{8 x^{3}} \times \sqrt{10 x^{4}} - 2 x \sqrt{8 x^{3}} \times \sqrt{5 x^{2}}$$
Rewrite the expression using $$\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$$:$$6 \sqrt{8 x^{3} \times 10 x^{4}} - 2 x \sqrt{8 x^{3} \times 5 x^{2}}$$
Multiply the monomials:$$6 \sqrt{80 x^{7}} - 2 x \sqrt{40 x^{5}}$$
Factor and rewrite the radicand in exponential form:$$6 \sqrt{4^{2} \times 5 x^{6} \times x} - 2 x \sqrt{2^{2} \times 10 x^{4} \times x}$$
Rewrite the expression using $$\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}$$:$$6 \sqrt{4^{2}} \times \sqrt{x^{6}} \times \sqrt{5 x} - 2 x \times \sqrt{2^{2}} \times \sqrt{x^{4}} \times \sqrt{10 x}$$
Simplify the radical expression:$$6 \times 4 x^{3} \sqrt{5 x} - 2 x \times 2 x^{2} \sqrt{10 x}$$,$$x \geq 0$$
Multiply the monomials:$$24 x^{3} \sqrt{5 x} - 4 x^{3} \sqrt{10 x}$$
Answer: $$24 x^{3} \sqrt{5 x} - 4 x^{3} \sqrt{10 x}$$