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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€