Question

What is the following simplified product? Assume x>/= 0

Answer 1

B

Explanation:

edg2021

Answer 2

Answer: second option.

Explanation:

We know that:

`\sqrt[n]{a^n}=a`

`(a^m)(a^n)=a^{(m+n)`

Then we can simplify the radicals:

`2√(8x^3)(3√(10x^4)-x√(5x^2))=(2√(2^2*2*x^2*x))(3√(10x^4)-x√(5x^2))=\\\\=2*2*x√(2x)=3x^2√(10)-x*x√(5)\\\\=4x√(2x)(3x^2√(10)-x^2√(5))`

Since:

`(a\sqrt[n]{x})*(b\sqrt[n]{y})=ab\sqrt[n]{xy}`

We can apply Distributive property:

`4x√(2x)(3x^2√(10)-x^2√(5))\\\\12x^3√(20x)-4x^3√(10x)`

Simplifying:

`12x^3*2√(5x)-4x^3√(10x)\\\\24x^3√(5x)-4x^3√(10x)`