Rules of Addition of like Terms 

In this lesson we will learn, how to add like terms.

Rule 1: In an expression, when all terms are positive, add their coefficients and variables and power of like terms remains the same.

Add like terms examples in expressions:

Example 1: Add like terms 2pq, 5pq, and 4pq.

Here, 2pq, 5pq, and 4pq are like terms.

= 2pq + 5pq + 4pq

The sum of the coefficients = 2 + 5 + 4 = 11  

Therefore, 2pq + 5pq + 4pq = 11pq

Example 2: Add like terms 6ab, 3ab, 9ab and 2ab.  

Here, 6ab, 3ab, 9ab and 2ab are like terms.

= 6ab + 3ab + 9ab + 2ab

The sum of the coefficients = 6 + 3 + 9 + 2 = 20  

Therefore, 6ab + 3ab + 9ab + 2ab = 20ab     

Example 3: Add 2x + 4x + 3y + 5y

Here, 2x and 4x are like terms and 3y and 5y are also like terms.

∴ 2x + 4x = 6x, and 3y + 5y = 8y

Therefore, the result is 6x + 8y  

Example 4: 8x³ + 5x³ + 3y²  + 2y² 

Here, 8x³ + 5x³  and 

3y²  + 2y² are like terms.  

∴ 8x³ + 5x³  = 11x³  and  

3y²  + 2y² = 5y² 

Therefore, the result is 11x³  + 5y²

Rule 2: In an expression, when all terms are negative, add their coefficient of without considering their negative sign and then prefix the minus sign to the sum.

Note: Be careful with the signs. if a term has a negative sign before it, consider it while adding/subtracting.

Example 1: Solve -3xy, -2xy,  and -5xy

Given terms are -3xy, -2xy,  and -5xy

The coefficients of the given terms are 3 + 2 + 5 = 10

Therefore, addition of -3xy, -2xy, and -5xy

= (-3xy) + (-2xy,) + (-5xy)

= -10xy

Therefore, the result is -10xy

Example 2: -2x, -5x,  -7y and -5y

Given terms are -2x, -5x,  -7y and -5y

Here, -2x, -5x,  are like terms, and -7y and -5y are also like terms.

= (-2x) + (-5x) + (-7y) + (-5y)

= (-2x) + (-5x)

= -7x  

= (-7y) + (-5y)

= -12y

Therefore, the result is -7x – 12y

Rule 3: If all terms have not same sign, the rule is same applied as for the addition of integers. 

Example 1: Add 15x and -8x

= 15x + (-8x)

= 15x – 8x

= 7x

Example 2: Solve  2x – 5x -7y + 5y 

adding and subtracting like terms

= 2x – 5x -7y + 5y

= -3x -2y

Example 3: Subtract 9xy from 5xy

5xy – 9xy

= -4xy

Examples of combining addition and subtraction of like terms:

Example 1: Combine like terms and simplify, 8x – 3y + 6xy – 4x + 7y – 9xy

arrange like terms

= 8x – 4x – 3y + 7y + 6xy – 9xy

= (8x – 4x) + (-3y + 7y) + (6xy – 9xy)

= 4x + 4y – 3xy 

Example 2: Combine like terms and simplify, 8xy – 3xy + 5xy – 4xy + 2xy – 9xy

arrange like terms

= 8xy – 3xy + 5xy – 4xy + 2xy – 9xy

= (8xy + 5xy + 2xy) + (-3xy – 4xy – 9xy)

= 15xy + (-16xy)

= 15xy + -16xy

= -xy