Question

HELP ASASP PLEASE!!!!!!! What is the following simplified product? Assume x>/0

Answer 1

Answer: Third option.
Please, see the detailed solution in the attache file.
Thanks

Answer 2

Answer:

Option 3 is correct answer i.e., $3x\sqrt{6x}-x^4\sqrt{30x}+24x^2\sqrt{2}-8x^5\sqrt{10}$

Step-by-step explanation:

Given: $(\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5})$

This Product is simplified using Polynomial Product of Binomial with Binomial.

Following are steps of Product:

$(\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5})$

⇒$(x\sqrt{6}+4\sqrt{4.2.x^2.x})(3\sqrt{x}-x\sqrt{5.x^4.x)}$

⇒$(x\sqrt{6}+8x\sqrt{2x})(3\sqrt{x}-x^3\sqrt{5x)}$

⇒ $(x\sqrt{6})(3\sqrt{x})+(x\sqrt{6})(-x^3\sqrt{5x})+(8x\sqrt{2x})(3\sqrt{x})+(8x\sqrt{2x})(-x^3\sqrt{5x})$

⇒$x.3\sqrt{6.x}+(-x.x^3\sqrt{6.5.x})+3.8x\sqrt{2x.x}+(-8x.x^3\sqrt{2x.5x})$

⇒$x3\sqrt{6x}-x^4\sqrt{30x}+24x\sqrt{2.x^2}-8x^4\sqrt{10.x^2}$

⇒$x3\sqrt{6x}-x^4\sqrt{30x}+24x.x\sqrt{2}-8x^4.x\sqrt{10}$

⇒$3x\sqrt{6x}-x^4\sqrt{30x}+24x^2\sqrt{2}-8x^5\sqrt{10}$

This Matches with Option 3.