Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power. For example, 8xyz2 and −5xyz2 are like terms because they have the same variables and power while 3abc and 3ghi are unlike terms because they have different variables. Since the coefficient doesn't affect likeness, all constant terms are like terms.
In this discussion, a "term" will refer to a string of numbers being multiplied or divided (remember that division is simply multiplication by a reciprocal) together. Terms are within the same expression and are combined by either addition or subtraction. For example, take the expression:
The known values assigned to the unlike part of two or more terms are called coefficients. As this example shows, when like terms exist in an expression, they may be combined by adding or subtracting (whatever the expression indicates) the coefficients, and maintaining the common factor of both terms. Such combination is called combining like terms, and it is an important tool used for solving equations.
The first step to grouping like terms in this expression is to get rid of the parentheses. Do this by distributing (multiplying) each number in front of a set of parentheses to each term in that set of parentheses:
The expression is considered simplified when all like terms have been combined, and all terms present are unlike. In this case, all terms now have different unknown factors, and are thus unlike, and so the expression is completely simplified.