There is a very simple property for adding and subtracting algebraic expressions. To be able to add or subtract expressions, we must have like terms. Like terms are terms that contain the same variable or group of variables raised to the same exponent, regardless of their numerical coefficient. For example:
3x and 6x are like terms. They both contain x.
6c^{2} and 19c^{2} are like terms. They both contain c^{2}.
2xy^{3} and 101xy^{3} are like terms. They both contain xy^{3}.
– km^{2}x^{5} and 17km^{2}x^{5} are like terms. They both contain km^{2}x^{5}.
Notice that to determine like terms, you must consider the variables in each term as a group. Like terms are those with exactly the same variables raised to the same exponent. If two terms have the same variables, but to different powers, they are not like terms and cannot be combined. For example:
x^{4} and 3x^{2} are not like terms since one contains x^{4} and the other contains x^{2} as variables.
5vk^{3} and vk^{2} are not like terms since one contains vk^{3} and the other contains vk^{2} as variables
To combine like terms, do the following:

For example, 3x + 6x can be simplified to (3 + 6) x = 9x
If possible, simplify each of the following expressions.
(1) 10a + 10b – 3a = 7a + 10b
To find the solution:

10a + 10b – 3a 

(10 – 3) a + 10b 

7a + 10b 
(2) 5b^{2} + 8b^{3} = 5b^{2} + 8b^{3}

5b^{2} + 8b^{3} 
(3) 3x^{2}y^{2}z – 5xyz + x^{2}y^{2}z = 4x^{2}y^{2}z – 5xyz

3x^{2}y^{2}z – 5xyz + x^{2}y^{2}z 

(3 + 1)(x^{2}y^{2}z) – 5xyz 

4x^{2}y^{2}z – 5xyz 
Combining like terms is crucial in solving equations. This is a procedure you will use often with algebraic expressions.
[introduction]  [exponents]  [multiply/divide]  [add/subtract]  [grouping] 