Theory:

Monomials that have the like products of the variable terms, even if the terms' order is different, are called similar monomials.
Example:
Similar monomials are:
 
05.PNG
 
and
 
06.PNG
07.PNG
and
08.PNG
09.PNG 
and
10.PNG
and
-3
11.PNG 
and
012.PNG
 
Non-similar monomials are, for example, 013.PNG and  014.PNG.
If similar monomials have the like coefficients, then these monomials are called mutually equal monomials.
If the monomials are mutually equal, it can be verified when the monomials are written in the standard form.
Example:
Out of these monomials
8xy3¯;xy3;8y3x¯;24xyyy¯;8x3y
 
mutually equal monomials are
8xy3;8y3x;24xyyy.
 
This can be proved if all the monomials are written in the standard form:
8xy3¯;xy3;8y3x¯;24xyyy¯;8x3y8xy3¯;xy3;8xy3¯;8xy3¯;8x3y
If the coefficients of similar monomials are the opposite numbers, then these monomials are called the opposite monomials.
Example:
Out of these monomials
3ac;9ab;3ac;abc;9ba
 
the opposite monomials are 3acand3ac;9baand9ba