Question

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

Answer 1

Option 3 is correct answer i.e.,
`3x√(6x)-x^4√(30x)+24x^2√(2)-8x^5√(10)`

Explanation:

Given:
`(√(6x^2)+4√(8x^3))(√(9x)-x√(5x^5))`

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

Following are steps of Product:

`(√(6x^2)+4√(8x^3))(√(9x)-x√(5x^5))`

⇒
`(x√(6)+4√(4.2.x^2.x))(3√(x)-x√(5.x^4.x))`

⇒
`(x√(6)+8x√(2x))(3√(x)-x^3√(5x))`

⇒
`(x√(6))(3√(x))+(x√(6))(-x^3√(5x))+(8x√(2x))(3√(x))+(8x√(2x))(-x^3√(5x))`

⇒
`x.3√(6.x)+(-x.x^3√(6.5.x))+3.8x√(2x.x)+(-8x.x^3√(2x.5x))`

⇒
`x3√(6x)-x^4√(30x)+24x√(2.x^2)-8x^4√(10.x^2)`

⇒
`x3√(6x)-x^4√(30x)+24x.x√(2)-8x^4.x√(10)`

⇒
`3x√(6x)-x^4√(30x)+24x^2√(2)-8x^5√(10)`

This Matches with Option 3.

Answer 2

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