Answer:
[tex]10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex]
Step-by-step explanation:
Remove perfect squares from under the radicals.
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\=(\sqrt{10x^4})(2\sqrt{15x^4}) +(\sqrt{10x^4})(\sqrt{3x^3}) -(x\sqrt{5x^2})(2\sqrt{15x^4}) -(x\sqrt{5x^2})(\sqrt{3x^3})\\\\=2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\=\boxed{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
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The applicable rules of exponents are ...
(x^a)(x^b) = x^(a+b)
√(a^2) = a . . . . . . . for a > 0
(√a)(√b) = √(ab)
