Explaining regular expressions folks. My question is about explaining the each step of regular expressions. The task is to find the regular expression that contains 101 as a substring. I already know that the regular expression for this is 

$$ (0 + 1)^*101(0 + 1)^*. $$

The question is that how we should show each step for explaining the regular expressions.
You have to show two things:


Every word in the language of your regular expression contains 101 as a substring.
Every word containing 101 as a substring belongs to the language of your regular expression.


You can prove both of these using the definition of the language of a regular expression. It is a bit tiring but otherwise requires little creativity.