Question

What is the following simplified product? Assume x>0 2 sqrt 8x^3(3 sqrt 10x^4-x sqrt 5x^2

Answer 1

Answer:B

Explanation:

It’s on edge

Answer 2

Answer:
`\bold{24x^3√(5x)-4x^3√(10x)}`

Explanation:

`2√(8x^3)\ (3√(10x^4)-x√(5x^2))\\\\2√(8x^3)\cdot 3√(10x^4)\ -\ 2√(8x^3)\cdot x√(5x^2)\quad \rightarrow \quad \text{applied distributive property}\\\\2\cdot 3√(8x^3\cdot10x^4)\ -\ 2\cdot x√(8x^3\cdot5x^2)\quad \rightarrow \quad \text{multiplied`

Evaluate each one separately:

`6\sqrt{\underline{2\cdot2}\cdot\underline{2\cdot2}\cdot5\cdot \underline{xx}\cdot \underline{xx}\cdot \underline{xx}\cdot x} = 6\cdot 2\cdot2\cdot x\cdot x\cdot x√(5x)=\boxed{24x^3√(5x)}\\\\2x\sqrt{\underline{2\cdot2}\cdot2\cdot5\cdot \underline{xx}\cdot \underline{xx}\cdot x}=2x\cdot 2\cdot x\cdot x√(2\cdot5\cdot x)=\boxed{4x^3√(10x)}`

The terms cannot be combined because they have different radicals (insides).

`\boxed{24x^3√(5x)}-\boxed{4x^3√(10x)}`