A. Like and unlike terms
Study the algebraic expression 2x + 5y + 7 + 3x + 9 + 2xy. It has 6 terms. Of these six terms the terms 2x and 3x have the same variable, that is x. So they are called like terms. Similarly 7 and 9 are both constants. They are also called like terms because they do not have a variable.

5y does not have a like term because no other term has the variable y. The term 2xy does not have a like term because no other term has the variables x and y.

Like terms

Two or more terms are called like terms if they have EXACTLY the same variables.

Example:

2x and 3x, 5y and −4y, 7xy and xy, 2xy² and 8xy² are like terms.

Note: Like terms can have different coefficients

But 2x and 2y, 5y and 5x, 7xy and 3xy², 2xy² and 8x²y are unlike terms.

B. Adding and subtracting algebraic expressions

To add or subtract algebraic expressions we use a similar method of adding and subtracting numbers. However, in the case of algebraic expressions, we need to sort and place the like terms and the unlike terms together which makes it easier to add or subtract.

Like terms can be added or subtracted by adding or subtracting their coefficients and taking the variable as it is.

Example:

2x and 3x are like terms. So 2x + 3x = (2 + 3) x = 5x.
7xy and xy are like terms. So 7xy – xy = (7 – 1)xy = 6xy.