Mathematics · Class 8
Factorisation
Common factors, regrouping, splitting middle term, and identities.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Factorisation writes expressions as products of factors — common factor, regrouping, using identities, and splitting middle term for quadratics — reverse of expansion.
Methods
- Common factor: 6x + 12 = 6(x + 2)
- Regrouping: ax + ay + bx + by
- Using identities: a²−b², (a±b)²
- Split middle term for ax² + bx + c
Identities for Factorisation
Difference of squares
a² − b² = (a+b)(a−b)
Perfect square
a² ± 2ab + b² = (a±b)²
Division of Polynomials
Factorise numerator and cancel common factors when dividing algebraic expressions.
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Common Factor
Factorise 4x² + 8x.
- 1HCF = 4x
- 24x(x + 2)
Answer
4x(x + 2)
Example 2: Identity
Factorise 9a² − 16b².
- 1(3a)² − (4b)²
- 2= (3a+4b)(3a−4b)
Answer
(3a + 4b)(3a − 4b)
Key Points to Remember
- ✓ Factorisation is not unique (constant factors)
- ✓ Check by expanding back
- ✓ Split middle term: find two numbers with sum b and product ac
Exam Tips
- • Take out HCF first always
- • Recognise perfect square trinomials
Practice MCQs — Factorisation
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Factor of 3x+6: