CommutatorExplicit[exp]
substitutes any Commutator
and AntiCommutator
in exp
by their definitions.
[a, b, c, d] DeclareNonCommutative
[a, b]
Commutator
[%] CommutatorExplicit
[a - c, b - d]
AntiCommutator
[%] CommutatorExplicit
[AntiCommutator[a - c, b - d]] // DotSimplify CommutatorExplicit
[a, b, c, d] UnDeclareNonCommutative