Adding polynomials is just a matter of combining like terms, with some order of operations considerations thrown in. As long as you're careful with the "minus" signs, and don't confuse addition and multiplication, you should do fine.
There are a couple formats for adding and subtracting polynomials, and they hearken back to the two methods you learned for addition and subtract of plain numbers, back when you were in grade school. First, you learned addition "horizontally", like this:
6 + 3 = 9
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That is, you were given relatively small values, and you learned to do the addition — largely in your head, and by working horizontally. We can add polynomials in the same way, grouping any "like" terms and then simplifying the results.
Simplify (2x + 5y) + (3x – 2y)
I'll clear the parentheses first. This is easy to do when adding, because there are no "minus" signs to take through any parentheticals. Then I'll group the like terms in accordance to their variables (keeping them in alphabetical order), and finally I'll simplify:
(2x + 5y) + (3x – 2y)
2x + 5y + 3x – 2y
2x + 3x + 5y – 2y
5x + 3y
These two terms are un-like (because they have different variables), so I cannot combine them. This means that I've gone as far as I can, so my hand-in answer is:
5x + 3y
