Like terms: Terms in an algebraic expression that have the same variable(s) raised to the same power. Only coefficients can differ.

Unlike terms: Terms with different variables or powers, meaning they cannot be combined.

Examples of like terms:

• 3x and 5x


• 2y² and -7y²


• 4ab and -9ab

Examples of unlike terms:

• 3x and 3y


• 2x² and 3x


• 5xy and 7x


• 4a and 4a²


• 6p and 7q


• 2m² and 3mn

Addition of Like Terms

Rule: Add or subtract only the coefficients; the variable(s) remain unchanged.

Worked Examples:

1. 3x + 5x = (3 + 5)x = 8x


2. 2y² + 7y² = (2 + 7)y² = 9y²


3. 5ab + 3ab = (5 + 3)ab = 8ab


4. 6m + 4m = 10m


5. -3x + 7x = 4x


6. 10p + (-4p) = 6p

Subtraction of Like Terms

Rule: Subtract the coefficients; the variable(s) remain the same.

Worked Examples:

1. 7x - 3x = 4x


2. 10y² - 6y² = 4y²


3. 9ab - 4ab = 5ab


4. 6m - 10m = -4m


5. 5x - (-3x) = 8x


6. -7p - 2p = -9p

Unlike Terms

Rule: Unlike terms cannot be added or subtracted because their variable(s) or powers are different.

Worked Examples:

1. 3x + 5y → Cannot combine, write as 3x + 5y


2. 2x² + 3x → Cannot combine, write as 2x² + 3x


3. 5xy + 7x → Cannot combine, write as 5xy + 7x


4. 4a + 4a² → Cannot combine, write as 4a + 4a²


5. 6p + 7q → Cannot combine, write as 6p + 7q


6. 2m² + 3mn → Cannot combine, write as 2m² + 3mn

Important Notes

• Only like terms can be combined.


• Unlike terms must remain separate.


• Always check the variable and its power before combining terms.