# Product of expectation values for multimode operators

If $A_{n}, B_{n'}, C^{\dagger}_{n''}, D^{\dagger}_{n'''}$ are multimode field operators that obey the bosonic commutation relations, under which circumstances the product of expectation values $\langle A_{n}B_{n'}\rangle \langle C^{\dagger}_{n''}D^{\dagger}_{n'''}\rangle$ can be expressed as $\langle A_{n}B_{n'}C^{\dagger}_{n''} D^{\dagger}_{n'''}\rangle$ ? Is this possible in the case of vacuum expectation values?