Does the Kleene star distribute over each element? (0+1)* = 0* + 1*? Does the Kleene star distribute over each element? Is this true: $(0+1)^* = (0^* + 1^*)$?
You can verify that $010$ is in $(0+1)^*$ but not in $(0^* + 1^*)$. Therefore, $(0 + 1)^* \neq (0^* + 1^*)$.