Finding a regular expression of a language Our alphabet is {a,b} and we need to find a regular expression for the language of all words of the form $a^*b^*$, whose length is a multiple of 3.

Obviously $(aaa)^*(bbb)^*$ is one of the options, but I just can't formalize more options.

Any help will be appreciated.
You have to put your triplets, and use Kleene star: $$(aaa)^*(bbb)^*$$

Now, add cases where number of $a$ is not divisible by 3, say aabbbb, as alternative.
$$ (aaa)^*(bbb)^* + (aaa)^*aab(bbb)^* + (aaa)^*abb(bbb)^*$$