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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, $(0 + 1)^* \neq (0^* + 1^*)$.
I believe this makes more sense:
$$ (0+1)^* = (0^*1^*)^* $$
$0^* + 1^*$ would limit the amount of strings covered.
Required, but never shown