Commutation Proof: Show That [Lx,L^2]=0 Cyclic

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Hi there, I need a help on one of the commutation proof,
the question is, show that [Lx,L^2]=0 cyclic where L=l1+l2
The expression simplifies to [Lx,l1l2]+[Lx,l2l1] but I'm not sure if they are 0.
Thanks for your help :D
 
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write L_x=L1_x+L2_x
and expand L^2=(L1+L2)^2=...
 

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