Like and Unlike Algebraic Terms      

Similar or Like Terms 

In an algebraic expression, like terms are terms that have same variables with same exponents and only the numerical coefficients of like terms are different. The terms must have the same variables and the same exponents.

3x, 7x, 8x, 12x, x, -4x, -9x  all are like terms because all terms has same variables, that is x and same exponent 1.

Example: 2x, -5x,  8x, all are like terms, because variables of all are same that is x. 

In the algebraic expression,

(1) -5xy + 8x + 2y + 5x, here  8x and 5x are like terms.

(2) 4x + 7y + 3y³ x² + 5y³ x^{2, here,}3y³ x² + 5y³ x² are like terms.

(3) y² x^{2 ,}  -3y² x²,  5y² x², are like terms.

In above examples, 

(1) -5xy + 8x + 2y + 5x

8x and 5x are like terms, because the variables are same that is x.

(2) 4x + 7y + 3y³ x² + 5y³ x², 

3y³ x² and 5y³ x², are like terms, because the variables are same that is y³ x² .

(3) y² x^{2 ,}  -3y² x²,  5y² x², are like terms, because the variables are same that is y² x² .

Dissimilar or Unlike Terms

In an algebraic expression, unlike terms are terms that do not have the same variables or powers are called the unlike terms.

5x and 8y are unlike terms, because the variables are not same that is x and y. 

Unlike Terms

Example: 2xz, -5x, 8y are unlike terms.

 y² x^{2 ,} 4x, 3xy, are unlike terms. 

In the algebraic expression

3xy + 8y + 2y + 9x  

3xy and 9x are unlike terms.

4x + 7y + 3y² x² + 5y² x²

4x and 7y are unlike terms.

In above examples, 

(1) 3xy + 8y + 2y + 9x

 3xy, and 9x are unlike terms, because the variables are not same, as xy, and x.

(2) 4x + 7y + 3y² x² + 5y² x²

4x and 7y, are unlike terms. 

4x and 7y are unlike terms, because the variables are not same that is x and y.

Note: We can only add or subtract like terms

                              Practice

  Identify like and unlike terms

 (1) 2a – 5b + 7c – 6a + 8a

 (2) 4x + 8yx + 2xy + 9x

 (3) 2xz + 7y + 5y² x² – 9y² x²

 (4) 4a²b² – 3y² x² + 4a²b²c² – a²b²    

 (5) 4m + 5yx + 3xy + 9x – 7mn + 2a

(6) 2x + 8mn + 2xy + 9x – 5mn

(7) -3y² x³ + 4a²b²c⁴ – a²b²  -7y² x³

(8) 4p + 5pq + 3xy + 9x 

(9) 2a – 5a + 7c – 6a + 8a

(10) a – b + c – a + a