$($a$)$ Let $=\{a,b\}.$ Write regular expression for the language L consisting of all strings in ${}^{*}$

that

i$.$ contain exactly one occurence of the substring $a$

ii$.$ contain exactly one occurence of the substring $aa$

iii. contain exactly one occurence of the substring aaa

$($b$)$ Simplify the following regex, explaining your reasoning

$((11{)}^{*}{1}^{*}{)}^{*}+(11+1{)}^{*}+(0+lon{)}^{*}$