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.
6c2 and 19c2 are like terms. They both contain c2.
2xy3 and 101xy3 are like terms. They both contain xy3.
km2x5 and 17km2x5 are like terms. They both contain km2x5.
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:
x4 and 3x2 are not like terms since one contains x4 and the other contains x2 as variables.
5vk3 and vk2 are not like terms since one contains vk3 and the other contains vk2 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) 5b2 + 8b3 = 5b2 + 8b3
||5b2 + 8b3|
(3) 3x2y2z 5xyz + x2y2z = 4x2y2z 5xyz
||3x2y2z 5xyz + x2y2z|
||(3 + 1)(x2y2z) 5xyz|
Combining like terms is crucial in solving equations. This is a procedure you will use often with algebraic expressions.