Regular expressions, is it always true that (r U s)* = r* U s* U (rs)*?
Consider the alphabet $\Sigma = \{a,b\}$, and the regular expressions $r = a$ and $s = b$. Then $(r+s)^* = \Sigma^*$ whereas $a^*+b^*$ and $a^*+b^*+(ab)^*$ are both smaller.