Computing $999,999\cdot 222,222 + 333,333\cdot 333,334$ by hand. I got this question from a last year's olympiad paper.

Compute $999,999\cdot 222,222 + 333,333\cdot 333,334$.

Is there an approach to this by using pen-and-paper?
EDIT Working through on paper made me figure out the answer. Posted below.
I'd now like to see other methods. Thank you.

$$999,999\cdot 222,222 + 333,333\cdot 333,334=333,333\cdot 666,666 + 333,333\cdot 333,334$$
$$=333,333 \cdot 1,000,000$$
