Create a regular expression for the language of all binary strings

such that

and

contains exactly one $1.$

The goal of this series of questions is to guide you through one possible approach to solving this problem. This is not the only approach, and we are not trying to suggest that it is the best approach.

Using the regular expressions you built in the previous part as cases, build a regular expression that describes this language.

$*$Hint: What operation do you use for language union?