I got this question from a last year’s olympiad paper.

Compute 999,999⋅222,222+333,333⋅333,334.

Is there an approach to this by using pen-and-paper?

EDITWorking through on paper made me figure out the answer. Posted below.I’d now like to see other methods. Thank you.

**Answer**

My observation suggests that we may simplify it somewhat like this assuming x=111,111:

9x⋅2x+3x(3x+1)=9x2+18x2+3x=27x2+3x=3x(9x+1)

So this means:

3x(9x+1)=333,333⋅(999,999+1)=333,333⋅1,000,000=333,333,000,000

**Attribution***Source : Link , Question Author : P.K. , Answer Author : OrangeDog*