Commutator Relation: What is [\hat{A}\hat{B}, \hat{C}\hat{D}] Equal to?

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What is the commutator [[itex]\hat{A}[/itex][itex]\hat{B}[/itex], [itex]\hat{C}[/itex][itex]\hat{D}[/itex]] equal to? How to distribute what's inside?
 
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=(ab)(cd)-(cd)(ab)
 
Fredrik said:
Use the rule [A,BC]=B[A,C]+[A,C]B. It's very easy to prove, so I suggest that you do that as an exercise.

Do you mean [A,BC]=[A,B]C+B[A,C]?