How is $ [(x+h)^{1/3} - x^{1/3}] [(x+h)^{2/3} +x^{1/3}(x+h)^{1/3}+ x^{2/3}] $ simplified to become $ (x+h-x) $?

Question

How is $ [(x+h)^{1/3} - x^{1/3}] [(x+h)^{2/3} +x^{1/3}(x+h)^{1/3}+ x^{2/3}] $ simplified to become $ (x+h-x) $ ??

I'm currently reading a text and I've been trying to get the hang of this for a while but I'm not understanding it. Can someone please explain.?

Answer 1

$$a^3-b^3=(a-b)(a^2+ab+b^2)$$ Replace $a=(x+h)^{\frac13}$ and $b=x^{\frac13}$.

Answer 2

Put $(x+h)^{1/3}=a\implies x+h=a^3$

and $x^{1/3}=b\implies x=b^3$

$$a^3-b^3=(a-b)(a^2+ab+b^2)$$