Adding and Subtracting Monomials
Definition of “like terms”: Two monomials with the same variables raised to the same powers are
considered “like terms” which may be added using the distributive property.
NOTE: The instruction “combine terms” is sometimes used to indicate addition or subtraction.
Example 1:
| a) 7x3 + 3x3 |
= (7 + 3)x3 |
Distributive property |
| |
= 10 x3 |
Add coefficients. |
| b) 9 x2y3 − 17 x2y3
|
= (9 − 17) x2y3 |
Distributive property |
| |
= − 8 x2y3 |
Subtract coefficients.
|
| c) 5 xy2 − 7 xy2 + 8 xy2 |
= (5 − 7 + 8) xy2 |
Distributive property |
| |
= 6 xy2 |
Add coefficients. |
d)
 |
= 9x5y3 − 3x5y3 |
Reduce each fraction. |
|
Don’t change exponents: |
= (9 − 3) x5y3 |
Distributive Property |
| = 6x5
y3 |
Add coefficients. |
| e) 3 x2y + 4 xy2 |
Cannot be added because the terms are not “like”
|
|