Opposite Monomials

Two monomials are considered opposite monomials if they have identical literal parts but numerical coefficients that are equal in absolute value and opposite in sign.

In other words, the literal part of each monomial is exactly the same.

Their coefficients have the same magnitude but opposite signs - that is, they are sign-opposite.

A concrete example

Consider the following pair of like terms:

$$ 3ab + (-3ab) $$

Let’s verify whether they meet all the criteria for being opposite monomials:

1. The literal part is the same: $$ ab $$
2. The coefficients have the same absolute value: $$ |3| = |-3| = 3 $$
3. The coefficients 3 and -3 have opposite signs, so they are sign-opposite.

All conditions are satisfied.

Therefore, the monomials 3ab and -3ab are opposite monomials.

Note: The algebraic sum of two opposite monomials is always zero. $$ 3ab + (-3ab) = 3 \cdot (ab - ab) = 3 \cdot 0 = 0 $$

And so on.