Combining ("Gathering") Like Terms
The terms of an expression are the parts of a mathematical expression that are separated by a plus (+) or minus (–) sign.
Each term is either a number or the product of a number (sometimes an understood 1) and one or more variables.
Example 1:
3x2y + 2xy – 9x + 2
The four terms of the expression are 3x2y, 2xy, 9x and 2.
Terms are like terms of their variable parts are the same.
Example 2:
3a and 4a are like terms.
7x2y and –9x2y are like terms but 7x2y and –9xy are unlike.
Like terms can be added or subtracted using the Distributive Property. The variable part stays the same; we just add the coefficients (the numerical portion of the terms). Unlike terms cannot be added or subtracted.
Example 3:
3a + 4a = (3 + 4)a = 7a
But, 3a + 4b cannot be added because they are unlike terms.
This is important when we simplify polynomials.
Example 4:
Simplify 6x2 + 5x + 4 – 4x2 + 7x – 8
Rearrange and group like terms using the Commutative and Associative Properties.
(6x2– 4x2) + (5x + 7x) + (4 – 8)
Use the Distributive Property to combine like terms.
(6 – 4)x2 + (5 + 7)x + (4 – 8)
= 2x2 + 12x – 4
