The language L $=\{$anbm $|$ n $>2,$ m $<2\}$

is not in the form of a regular expression. The regular expression is given by:

$($I$)$ aa$*(+$bb$*)$

$($II$)$ aaa$*(+$bb$*)$

$($III$)$ aaa$*(+$bb$)$

$($IV$)$ aaa$*(+$b$)$

$($V$)$ aa$*(+$b$)$