Like and unlike terms
When you visit a market, you can see that, the vegetables and fruits of same kind are kept as separate heaps. Similarly, we can group the same kind of terms in an algebraic expression.
For example, the expression 7x + 5x + 12x – 16 has 4 terms but the first three terms have the same variable factor x. We say that 7x, 5x and 12x are like terms.
However, the terms 12x and −16 have different variable factors. The term 12x has the variable x and the term −16 is a constant. Such terms are called unlike terms.
Consider another example. In the expression 14xy−7y−12yx+5y−10, the terms −7y and 5y are like terms. Also, 14xy and −12yx are like terms. But, we cannot group the terms 14xy, 7y and − 10, as they do not have the same variables, thus called unlike terms.
Hence, the terms of an expression having the same variable(s) are called like terms; otherwise, they are called unlike terms. The following activity is helpful in identifying the like terms and unlike terms.
Identify the like terms among the following and group them: 7xy, 19x, 1, 5y, x, 3yx, 15, –13y, 6x, 12xy, −5, 16y, −9x, 15xy, 23, 45y, −8y, 23x, −y, 11.
Like terms :
7xy, 3yx, 12xy, 15 xy
19x, x, 6x, –9x, 23x
5y, –13y, 16y, 45y, –8y, –y
1, 15, –5, 23, 11
Terms with the variables xy and yx are like terms, because of the commutative property of multiplication x × y = y × x. Also, terms obey the commutative property of addition, that is x + y = y + x.
Points to remember while identifying like terms are as follows:
(i) In each of the term ignore numerical co-efficient.
(ii) Observe the algebraic variables of the terms. They must be the same. (Here the order in which the variables are multiplied should not be considered).