Collecting Like Terms
GCSE Mathematics🧩 What are Like Terms?
Like terms are terms that have exactly the same variables raised to the same powers. Collecting (or combining) like terms means adding or subtracting terms that are the same to simplify expressions. Think of it as grouping identical items together - like counting all the apples separately from oranges.
🎨 Visual Representation
3x + 2y (3 x's and 2 y's)
2x + y (2 x's and 1 y)
5x + 3y (5 x's and 3 y's)
📚 How to Collect Like Terms
🔹 Basic Like Terms (Same Variable)
Combine terms with the same variable by adding or subtracting their coefficients.
Example 1
3x + 5x
= (3 + 5)x
= 8x
Example 2
7y - 2y
= (7 - 2)y
= 5y
Example 3
4a + a
= 4a + 1a
= 5a
➕➖ With Positive and Negative Signs
Pay attention to the signs before each term.
Example 1
4x - 2x + 3x
= (4 - 2 + 3)x
= 5x
Example 2
-3y + 7y - 2y
= (-3 + 7 - 2)y
= 2y
Example 3
5a - 3a - a + 4a
= (5 - 3 - 1 + 4)a
= 5a
⬆️ Terms with Powers (Exponents)
Terms are only like if they have the same variable AND the same power.
Example 1
3x² + 5x²
= (3 + 5)x²
= 8x²
Example 2
7y³ - 2y³
= (7 - 2)y³
= 5y³
Example 3
4x² + 3x - 2x² + x
= (4x² - 2x²) + (3x + x)
= 2x² + 4x
🔄 Mixed Terms with Multiple Variables
Group terms with the same variable combinations.
Example 1
3x + 2y + 5x - y
= (3x + 5x) + (2y - y)
= 8x + y
Example 2
4a + 3b - 2a + 5b - a
= (4a - 2a - a) + (3b + 5b)
= a + 8b
Example 3
2x² + 3xy - x² + 4xy
= (2x² - x²) + (3xy + 4xy)
= x² + 7xy
🔄 Interactive Like Terms Sorter
Drag and drop (or click) to sort terms into groups:
x terms
y terms
x² terms
xy terms
✏️ Practice Collecting Like Terms
Simplify: 4x + 3y - 2x + 5y
⚠️ Common Mistakes to Avoid
❌ Wrong: Combining unlike terms
3x + 2y = 5xy ❌
Correct: 3x + 2y (cannot combine - different variables)
✅ Correct: Only combine like terms
3x + 2x = 5x ✓
4y - y = 3y ✓
❌ Wrong: Forgetting the invisible 1
x + 2x = 2x ❌ (forgot x is 1x)
Correct: x + 2x = 3x
⚠️ Careful with signs!
3x - 5x + 2x
= (3 - 5 + 2)x = 0x = 0
🌍 Real-World Connection
Collecting like terms is like organizing items in real life:
🛒 Shopping List
3 apples + 2 oranges + 5 apples - 1 orange
= (3 + 5) apples + (2 - 1) oranges
= 8 apples + 1 orange
💰 Money
£5 + €3 + £2 - €1
= (£5 + £2) + (€3 - €1)
= £7 + €2
📦 Inventory
4 boxes + 3 crates + 2 boxes - 1 crate
= (4 + 2) boxes + (3 - 1) crates
= 6 boxes + 2 crates