Answer:
Option 3 is correct answer i.e., [tex]3x\sqrt{6x}-x^4\sqrt{30x}+24x^2\sqrt{2}-8x^5\sqrt{10}[/tex]
Step-by-step explanation:
Given: [tex](\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5})[/tex]
This Product is simplified using Polynomial Product of Binomial with Binomial.
Following are steps of Product:
[tex](\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5})[/tex]
⇒[tex](x\sqrt{6}+4\sqrt{4.2.x^2.x})(3\sqrt{x}-x\sqrt{5.x^4.x)}[/tex]
⇒[tex](x\sqrt{6}+8x\sqrt{2x})(3\sqrt{x}-x^3\sqrt{5x)}[/tex]
⇒ [tex](x\sqrt{6})(3\sqrt{x})+(x\sqrt{6})(-x^3\sqrt{5x})+(8x\sqrt{2x})(3\sqrt{x})+(8x\sqrt{2x})(-x^3\sqrt{5x})[/tex]
⇒[tex]x.3\sqrt{6.x}+(-x.x^3\sqrt{6.5.x})+3.8x\sqrt{2x.x}+(-8x.x^3\sqrt{2x.5x})[/tex]
⇒[tex]x3\sqrt{6x}-x^4\sqrt{30x}+24x\sqrt{2.x^2}-8x^4\sqrt{10.x^2}[/tex]
⇒[tex]x3\sqrt{6x}-x^4\sqrt{30x}+24x.x\sqrt{2}-8x^4.x\sqrt{10}[/tex]
⇒[tex]3x\sqrt{6x}-x^4\sqrt{30x}+24x^2\sqrt{2}-8x^5\sqrt{10}[/tex]
This Matches with Option 3.
