# How this simplification works in “addition”?

I have this:

j + k = (2a + 1) + (2b + 1)

j + k = 2a + 2b + 2

Is the extra 2 (in the second line) came from the sum of the two ones? What if I have this:

j + k = (3a + 3) + (4b + 3)

would be OK to simplify it like this

j + k = 3a + 4b + 6

Or there is a rule for that?

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Yes, the $2$ comes from adding the two $1$s. Yes, it's correct to simplify to $3a+4b+6$. – Jeff Mar 12 '12 at 5:26

$$\rm (a+b)+c=a+(b+c) \qquad\qquad a+b=b+a.$$
This ensures that parentheses, in the context of addition, are superfluous and can be invoked or discarded at will, and that summands can be permuted arbitrarily at will. Thus, e.g. $$\rm (2a+1)+(2b+1)=2a+1+2b+1=2a+2b+(1+1)=2a+2b+2.$$