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.

My first (useful) though was factoring out 333,333:
$$\begin{align*}
&999,999*222,222+333,333*333,334 =\\
&= 333,333*(3*222,222+333,334) =\\
&= 333,333*(666,666+333,334) =\\
&= 333,333*1,000,000 =\\
&= 333,333,000,000
\end{align*}$$
