Could someone explain to me how the author goes from 2nd to 3rd step(adsbygoogle = window.adsbygoogle || []).push({});

I think the intermediate step between 2 and 3 is basically to split up the commutator as

[y p_z, z p_x] - [y p_z,x p_z] - [z p_y,z p_x] + [z p_y, x p_z]

2nd term = 0

3rd term = 0

so leftover is

[L_x, L_y] = [y p_z, z p_x] + [z p_y, x p_z]

but how does this turn into what he has on 3rd step?

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# Basic commutator of angular momentum

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