-Subscript[A, 111]^2 Subscript[B, 211]^2 + Subscript[A, 111]^2 Subscript[CC, 211]^2 - 2 Subscript[A, 111] Subscript[A, 211] Subscript[CC, 111] Subscript[ CC, 211] + Subscript[A, 211]^2 Subscript[CC, 111]^2 + Subscript[B, 211]^2 Subscript[CC, 111]^2;
AA = {Subscript[A, 111], Subscript[A, 211]}; BB = {Subscript[B, 111], Subscript[B, 211]}; CC = {Subscript[C, 211], Subscript[C, 111]}; wAsymm = {{1, -1}, {-1, 1}}; Tr[ (wAsymm*Outer[Times, AA, AA]) . Outer[Times, CC, CC] ]
B