Combining ("Gathering") Like Terms
First, we'll define what "terms" are. Then we'll see what "like terms" are.
A term is a product of a number and some variables, like 3xy or –4x2. If the variable part is the same in two terms, they're called like terms.
Examples:
3x and 5x are like terms; 3x and 5y are unlike terms.
7a3b and 99a3b are like terms; 7ab and 99ab2 are unlike.
If two terms are "like" then you can add or subtract them. Notice the use of the Distributive Property here.
3x + 5x = (3 + 5)x = 8x
The variable part stays the same; we can just add the coefficients (the numbers in front of the variables).
But unlike terms can't be added.
3x + 4y ≠ 7x or 7y or 7xy, and
6 + 5x ≠ 11x.
(The symbol ≠ means "not equal to.")
This is important when simplifying polynomials.
Example:
Simplify.
6x2 + 5x + 4 – 4x2 + 7x – 8
First, collect the like terms in parentheses.
= (6x2 – 4x2) + (5x + 7x) + (4 – 8)
Then simplify.
= 2x2 + 12x – 4
