Answer:
![32x^2\sqrt[3]{2x} -8x^3](https://tex.z-dn.net/?f=32x%5E2%5Csqrt%5B3%5D%7B2x%7D%20-8x%5E3)
Step-by-step explanation:
To multiply radicals of the same index, we multiply the coefficient of the radicals together and the radicands (the things inside the radical) together.
![4x\sqrt[3]{4x^2} (2\sqrt[3]{32x^2} -x\sqrt[3]{2x} )](https://tex.z-dn.net/?f=4x%5Csqrt%5B3%5D%7B4x%5E2%7D%20%282%5Csqrt%5B3%5D%7B32x%5E2%7D%20-x%5Csqrt%5B3%5D%7B2x%7D%20%29)
![(4x)(2)\sqrt[3]{(4x^2)(32x^2)} -(4x)(x)\sqrt[3]{(4x^2)(2x)}](https://tex.z-dn.net/?f=%284x%29%282%29%5Csqrt%5B3%5D%7B%284x%5E2%29%2832x%5E2%29%7D%20-%284x%29%28x%29%5Csqrt%5B3%5D%7B%284x%5E2%29%282x%29%7D)
![8x\sqrt[3]{128x^4} -4x^2\sqrt[3]{8x^3}](https://tex.z-dn.net/?f=8x%5Csqrt%5B3%5D%7B128x%5E4%7D%20-4x%5E2%5Csqrt%5B3%5D%7B8x%5E3%7D)
Remember that
,
, and
, so:
![8x\sqrt[3]{(2^6)(2)(x^3)(x)} -4x^2\sqrt[3]{2^3x^3}](https://tex.z-dn.net/?f=8x%5Csqrt%5B3%5D%7B%282%5E6%29%282%29%28x%5E3%29%28x%29%7D%20-4x%5E2%5Csqrt%5B3%5D%7B2%5E3x%5E3%7D)
Remember that radicands with the same index (or evenly divisible by the index) can be taken out the radical, so:
![(2^2)(x)(8x)\sqrt[3]2{x} -(4x^2)(2x)](https://tex.z-dn.net/?f=%282%5E2%29%28x%29%288x%29%5Csqrt%5B3%5D2%7Bx%7D%20-%284x%5E2%29%282x%29)
![32x^2\sqrt[3]{2x} -8x^3](https://tex.z-dn.net/?f=32x%5E2%5Csqrt%5B3%5D%7B2x%7D%20-8x%5E3)
We can conclude that the second choice is the correct answer.