Algebraic Expressions • Topic 3 of 3

Combining Like Terms

What are Like Terms?

Like terms are terms that have the exact same variable raised to the exact same power.

Like Terms Examples:

3x and 5x (same variable x)
2y² and 7y² (same y²)
4 and 9 (constants with no variable)

NOT Like Terms:

3x and 3y (different variables)
2x and 2x² (different exponents)

How to Combine Like Terms:

Add or subtract the coefficients (numbers in front), keep the variable the same.

3a + 5a = (3 + 5)a = 8a
7b - 2b = (7 - 2)b = 5b
4x² + 2x² = (4 + 2)x² = 6x²

COMBINING LIKE TERMS - VISUAL:

    3 apples + 5 apples = 8 apples
    
    3a + 5a = 8a ✓


    3 apples + 5 bananas cannot combine
    
    3a + 5b stays 3a + 5b ✗


LIKE TERMS SORTING BOX:

    Expression: 5x + 3y + 2x + 4y - 2
    
    Sort into like terms:
    
    ┌─────────────┬─────────────┬─────────────┐
    │   x terms   │   y terms   │  Constants  │
    ├─────────────┼─────────────┼─────────────┤
    │    5x       │    3y       │      -2     │
    │   +2x       │   +4y       │             │
    ├─────────────┼─────────────┼─────────────┤
    │    7x       │    7y       │      -2     │
    └─────────────┴─────────────┴─────────────┘
    
    Simplified: 7x + 7y - 2


COMBINING - STEP BY STEP:

    Expression: 4x + 2 + 3x + 5
    
    Step 1: Identify like terms
    x terms: 4x and 3x
    constants: 2 and 5
    
    Step 2: Combine x terms
    4x + 3x = 7x
    
    Step 3: Combine constants
    2 + 5 = 7
    
    Step 4: Write simplified expression
    7x + 7

Solved Examples

Worked Example

Combine like terms: 7a + 3a

Solution

Both have variable a
7 + 3 = 10
Answer: 10a

Worked Example

Combine like terms: 4x + 2x + 5

Solution

x terms: 4x + 2x = 6x
Constant: +5 stays
Answer: 6x + 5

Worked Example

Combine like terms: 3y + 8 - 2y + 4

Solution

y terms: 3y - 2y = 1y (or just y)
Constants: 8 + 4 = 12
Answer: y + 12

Worked Example

Combine like terms: 5x² + 2x + 3x² - x

Solution

x² terms: 5x² + 3x² = 8x²
x terms: 2x - x = 1x (or x)
Answer: 8x² + x

Worked Example

Combine like terms: 2a + 3b + 4a - b

Solution

a terms: 2a + 4a = 6a
b terms: 3b - b = 2b
Answer: 6a + 2b

Key Points

Like terms have same variable AND same exponent
Coefficients add/subtract; variables stay the same
Constants combine with constants
Unlike terms cannot be combined
Always simplify by combining like terms when possible

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.$3x+2x=$

Explanation: Add coefficients.

Q2.Like terms have the same:

Explanation: Same variable.

Q3.$5a-2a=$

Explanation: $3a$.

Q4.$4x$ and $3y$ are:

Explanation: Unlike.

Practice more MCQs → 📝 Assignment · 35 marks