Combining Like Terms
Like Terms- Terms that have the same VARIABLE AND the same EXPONENT. (Example: x2 can only be combined with x2, x can only be combined with x; units can only be combined with units)
When you are Adding:
Use your ADDITION Integer Rules (same sign add and keep, different sign subtract and take the sign of the larger digit) to combine your like terms.
Ex1) 3x2 +2x – 5
+ 5x –3
3 x2 + 7x – 8
Ex2. 7x2 –5 + 3x –4 + x2 –1
Using your ADDITION integer rules: You can combine 7x 2 with x2 to make 8x2 ; You can combine +3x with nothing else since there are no more xs; You can combine –5 with –4 and –1 for a total of –10. So your simplified version of the above expression would be:
8x2 +3x –10
NOTE: The Commutative Property states that you an change the order so any variation of the above answers (as long as the signs are the same would be acceptable (ex. -10 + 3x + 8x2)
Subtracting
If you have a negative sign directly outside parentheses, you must distribute the negative to everything inside parentheses. Therefore you must change all your signs inside parentheses to the opposite sign FOLLOWING YOUR MULTIPLICATION INTEGER RULES! (Same signs when multiplied = positive; Different signs when multiplied = a negative).
Ex1. (3x2 -2x +5) – (7x2 –x +1) becomes 3x2 -2x +5 – 7x2 +x -1
After the negative is distributed you follow your ADDITION Integer Rules to combine your like terms as usual so your final answer would be: -4x2 –x +4
Ex 2.
4x2 - 5x +1
- 3x2 +6x -3
In this case, you see a negative as the very first sign on the second line. You can think of this as subtracting everything on the second line from everything on the top line. We know that Subtraction is like ADDING the OPPOSITE, so you change the subtraction sign to addition then change ALL signs on the second line ONLY to the opposite sign so…
4x2 - 5x +1
(-)3x2 +6x -3
Becomes
4x2 - 5x +1
- 3x2 -6x +3
You then can combine your like terms following your ADDITION Integer Rules to combine your like terms. So your final answer would be :
4x2 - 5x +1
-3x2 -6x +3
1x2 -11x +4