A=aa* = $a^{+}$ = set of all strings of a's with one or more a
B= bb*=$b^{+}$ = set of all strings of b's with one or more b
we know that,
If R1 and R2 are regular expressions, then R1 | R2 (also written as R1 U R2 or R1 + R2) is also a regular expression.
so (AUB)*=( $a^{+}$ + $b^{+}$)* =(a+b)*
so option 3 is correct.