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

Step-by-step explanation:

It’s on edge

Answer 2

Answer:   $\bold{24x^3\sqrt{5x}-4x^3\sqrt{10x}}$

Step-by-step explanation:

$2\sqrt{8x^3}\ (3\sqrt{10x^4}-x\sqrt{5x^2})\\\\2\sqrt{8x^3}\cdot 3\sqrt{10x^4}\ -\ 2\sqrt{8x^3}\cdot x\sqrt{5x^2}\quad \rightarrow \quad \text{applied distributive property}\\\\2\cdot 3\sqrt{8x^3\cdot10x^4}\ -\ 2\cdot x\sqrt{8x^3\cdot5x^2}\quad \rightarrow \quad \text{multiplied "outsides" and "insides"}$

Evaluate each one separately:

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

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

$\boxed{24x^3\sqrt{5x}}-\boxed{4x^3\sqrt{10x}}$