Difference between 1* + 0* and (1 + 0)*
The set $1^*+0^*$ is composed of two parts: $1^*$ and $0^*$. The first part, $1^*$, is all strings composed entirely of $1$s. The second part, $0^*$, is all strings composed entirely of $0$s. In contrast, $(1+0)^*$ is all strings composed of $0$s and $1$s. Can you now think of a string in $(1+0)^*$ but not in $1^*+0^*$?