1234567890
x 111111
------------
1234567890
12345678900
123456789000
1234567890000
12345678900000
+ 123456789000000
-----------------
137,174,072,825,790
...looks like O(n^2).
Once the longer number starts repeating digits, then it's not n^2 anymore. Multiplies get replaced with lookups. And we're only counting the multiplies. That's all they counted in the article. Not the adds, not the shifts.