← Chapter 48 Chapter 49: Factorising Expressions Chapter 50 →

Chapter 49: Factorising Expressions

✏️ Explanation

Factorising is the reverse of expanding brackets. Find the common factor and take it outside brackets.

🔍 Why It Matters

Factorising simplifies expressions and is essential for solving quadratic equations and advanced algebra.

✏️ Worked Example

Factorise: 6x + 9
Step 1: Find the common factor
Common factor is 3
Step 2: Divide each term by the common factor
6x ÷ 3 = 2x, 9 ÷ 3 = 3
Step 3: Write with factor outside brackets
6x + 9 = 3(2x + 3)

🔢 Practice Exercises

1. Factorise: 4x + 8
Answer:
2. Factorise: 6y - 15
Answer:
3. Factorise: 10a + 5b
Answer:
4. Factorise: 3x² + 12x
Answer:
5. Factorise: 8xy - 4x
Answer:

⚠️ Common Mistakes

  • Not finding the highest common factor
  • Forgetting to check by expanding
  • Missing variables in common factors

✨ Quick Summary

Find the biggest common factor and put it outside brackets. Check by expanding.