Not necessarily an error. Just a competing methodology that is in dispute. I love this debate. The "2" people (including myself) are subscribing to the view that the 2(9+3) demonstrates a multiplication by juxtaposition which would take precedence over "normal" multiplication.
I provided an earlier cite for this at
Ask Dr. Math where he states:
The closest thing I have found is the convention used by the _Mathematical Reviews_ of the American Mathematical Society (AMS), at
Mathematical Reviews Database - Guide for Reviewers http://www.ams.org/authors/guide-reviewers.html
that "multiplication indicated by juxtaposition is carried out before division." Thus, in general, for any variables a, b and c, we would have a/bc = a/(bc) (assuming, of course, that b and c are nonzero).
However, the ams link is dead and I didn't track it down any further.
It's actually fascinating to see such debate at physics forums and math forums about this very issue...an issue that one little "(" would solve. To me, the 2(9+3) represents a 2 that was factored out of the 9+3 originally, so would be represented as ((9*2)+(3*2)).
The juxtaposition angle is something I'm going to keep looking into, I can't believe I've found a math-related argument so interesting.
Yes, it is interesting that some mathematicians seem to have this juxtaposition rule. Keep in mind that they are referring to algebraic expressions, like 2/4x, and not simple math problems like we have here.
But engineers program the software and the consensus there is that there is no juxtaposition rule.
We should all be able to agree that this question is poorly defined and that parentheses are our friends.