Abstract: The expansion results of the commutation relation of multi-operators multiplication are studied，and a universal expansion formula is found. The formula can be proved strictly，and the proof process is also shown. The formula can directly show the expansion result of the commutation relation for multi-operators multiplication. The formula is used to expand the commutation relation of some common quantum mechanics operators. The expanded results using the formula are the same as that obtained through the normal procedure. These results further confirm the correctness of the formula.

Key words: commutation relation, multi-operator multiplication, universal formula, mathematical induction