Question

What is the following simplified product? Assume x>/0 (sqrt 10x^4 - x sqrt 5x^2)(2sqrt 15x^4 + sqrt 3x^3 )

Answer 1

Answer: D on edge

Step-by-step explanation: just took the test

Answer 2

Option D is correct.

Explanation:

We have to simplify the following product as given in the question :

`(\sqrt{10x^(4)} - x\sqrt{5x^(2)})(2\sqrt{15x^(4)} + \sqrt{3x^(3) } )`

=
`(\sqrt{10x^(4)} - \sqrt{5x^(4)})(\sqrt{60x^(4)} + \sqrt{3x^(3)})`

{Keeping all the terms within square roots}

=
`(\sqrt{10x^(4)})(\sqrt{60x^(4)}) + (\sqrt{10x^(4)})(\sqrt{3x^(3)}) - (\sqrt{5x^(4)})(\sqrt{60x^(4)}) - (\sqrt{5x^(4)})(\sqrt{3x^(3)})`

{By distributive property of multiplication}

=
`\sqrt{600x^(8)} + \sqrt{30x^(7)} - \sqrt{300x^(8)} - \sqrt{15x^(7)}`

=
`10x^(4)√(6) + x^(3)√(30x) - 10x^(4)√(3) - x^(3)√(15x)`

Therefore, option D is correct. (Answer)