Regular expression for the language containing neither aa nor bb I want to create a regular expression for the language

$L=\{ w \in \{a,b\} |$ w has neither aa nor bb as a subword$\}$.

I've tried various things, but I can't seem to get the correct regular expression.
$((ab)^∗∪(ab)^∗a)∪((ba)^∗∪(ba)^∗b)$  will work.

The possibilities are: $a,ab,aba,ababa,...$ or $b,ba,bab,baba,...$ or empty string