Definition
Like terms
Like terms have exactly the same variable factors, with the same exponents.
Continue from this idea into connected AXIO math.
Defining relationship
Match the letter-and-exponent pattern; the front numbers may differ.
Like terms are algebraic terms whose variable parts are identical after standard ordering: the same variables are raised to the same powers. Their numerical coefficients may be different, so their coefficients can be added or subtracted.
- 1
same variable part x
- 2
combine only coefficients
- 3
simplified like term
- Variable letters match
- Exponents match
What it means
Ignore the number in front and compare the letter part. 7x and −2x belong together because both have x. But 7x and 7x² do not, because x and x² are different variable parts. Like terms can be combined without changing the variable part.
Remember it
Match the letter-and-exponent pattern; the front numbers may differ.
Example
Simplify 6a + 3 − 2a + 5. The a-terms are like, so 6a − 2a = 4a. The constants are also like, so 3 + 5 = 8. The result is 4a + 8.
Watch for
4x and 4y are not like terms; matching coefficients do not make the variable parts match.
Common mix-up
xy and yx are like terms because multiplication can be reordered, but x and x² are not like terms.
Exact meaning
Like terms are algebraic terms whose variable parts are identical after standard ordering: the same variables are raised to the same powers. Their numerical coefficients may be different, so their coefficients can be added or subtracted.