Regular expression for strings with an even number of zeroes and ones

Question

What is a regular expression for strings of 0 and 1 with an even number of zeros and an even number of ones?

I have something like (1*01*01*)*(0*10*10*)*

Answer 1

Well, this is probably homework, but what the heck:

^(00|11|(01|10)(00|11)*(01|10))*$

Edit: simplified!