You cannot apply the rules of algebra to arithmetic. There are no variables or coefficients in arithmetic. 2(1+2) is not a unit, and there is no rule in any textbook that makes it so! The 2 is not a coefficient of the parenthesis. Evaluating the parenthesis means doing the operations INSIDE the (). It does not involve any multiplication by outside numbers. Nothing outside the parenthesis is connected to it. Also this is arithmetic, not algebra. By substituting a variable for the entire parenthesis you have completely changed the expression. variables are not treated the same as numbers, because variables cannot be added to or multiplied by numbers to form single quantities. (2+1)=3. (x+y) is just (x+y) it cannot be reduced. 2(x+y) can only be simplified to 2x + 2y. it cannot be fully resolved!