Answer:
[tex] 24x^3\sqrt{5x} - 4x^3\sqrt{10x} [/tex]
Step-by-step explanation:
The product [tex]2\sqrt{8x^3} (3\sqrt{10x^4} - x\sqrt{5x^2})[/tex] can be simplified as follows:
Step 1: Use the distributive property of multiplication
[tex]2\sqrt{8x^3}(3\sqrt{10x^4)} - 2\sqrt{8x^3}(x\sqrt{5x^2})[/tex]
[tex] 2*3\sqrt{8x^3*10x^4} - 2*x\sqrt{8x^3*5x^2} [/tex]
[tex] 6\sqrt{80x^7} - 2x\sqrt{40x^5} [/tex]
Step 2: simplify further
[tex] 6\sqrt{16*5*x^3*x^3*x} - 2x\sqrt{4*10*x^4*x} [/tex]
[tex] 6*4*x^3\sqrt{5*x} - 2x*2*x^2\sqrt{10*x} [/tex]
[tex] 24x^3\sqrt{5x} - 4x^3\sqrt{10x} [/tex]
