For linear operators A, B, and C, show that [A,BC] = [A,B]C + B[A,C].
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For linear operators Aˆ, Bˆ, and Cˆ, show that [Aˆ,BˆCˆ] = [Aˆ,Bˆ]Cˆ + Bˆ[Aˆ,Cˆ].
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