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Adding and Subtracting Monomials
Definition of “like termsâ€: 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
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