Adding and Subtracting Monomials
Definition of â€œlike termsâ€: Two monomials with the same variables raised to the same powers are
considered â€œlike termsâ€ which may be added using the distributive property.
NOTE: The instruction â€œcombine termsâ€ is sometimes used to indicate addition or subtraction.
Example 1:
a) 7x^{3} + 3x^{3} 
= (7 + 3)x^{3} 
Distributive property 

= 10 x^{3} 
Add coefficients. 
b) 9 x^{2}y^{3} − 17 x^{2}y^{3}

= (9 − 17) x^{2}y^{3} 
Distributive property 

= − 8 x^{2}y^{3} 
Subtract coefficients.

c) 5 xy^{2} − 7 xy^{2} + 8 xy^{2} 
= (5 − 7 + 8) xy^{2} 
Distributive property 

= 6 xy^{2} 
Add coefficients. 
d)

= 9x^{5}y^{3} − 3x^{5}y^{3} 
Reduce each fraction. 
Donâ€™t change exponents: 
= (9 − 3) x^{5}y^{3} 
Distributive Property 
= 6x^{5}
y^{3} 
Add coefficients. 
e) 3 x^{2}y + 4 xy^{2} 
Cannot be added because the terms are not â€œlikeâ€
