Class 8MathematicsChapter 14Preksha • Last-Minute Revision
Factorisation
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- Factorisation writes an expression as a product.
- Look for a common factor first.
- Regrouping can create a common binomial factor.
- Difference of squares factors as (a+b)(a-b).
- Multiplication is the best check of a factorisation.
What You Will Learn
- Understand factorisation as reverse multiplication
- Take common factors
- Factorise by regrouping
- Use identities to factorise
- Check factors by multiplying back
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
Reverse multiplication
If 3x(x+2)=3x²+6x, then 3x²+6x=3x(x+2). Factorisation reverses expansion.
Common factor
Take the greatest numerical and algebraic factor common to all terms before trying other methods.
Regrouping
Group terms so that a common bracket appears, then factor that common bracket.
Identity method
Recognise perfect-square trinomials and differences of squares quickly.
Middle-term pattern
Expressions such as x²+(a+b)x+ab factor as (x+a)(x+b).
Formula Sheet
Formula / Key Relations
Perfect square
Recognise first and last squares.
Perfect square
Middle term is negative.
Difference of squares
No middle term.
Binomial pattern
Find numbers with correct sum and product.
Worked Examples
Common factor
Question
Factorise 8x²y + 12xy².
Solution
Take out 4xy.
Quadratic pattern
Question
Factorise x²+7x+12.
Solution
3+4=7 and 3×4=12.
Exam Traps
Quick Revision
Quick Revision
- Factorisation writes an expression as a product.
- Look for a common factor first.
- Regrouping can create a common binomial factor.
- Difference of squares factors as (a+b)(a-b).
- Multiplication is the best check of a factorisation.
- Revise the formula sheet once more before attempting questions.
Compact Practice
Q1MCQModerateClass 8
Factorise 6x+12.
View Solution
6(x+2)
Q2ShortModerateClass 8
x²-25?
View Solution
(x+5)(x-5)
Q3ShortModerateClass 8
x²+9x+20?
View Solution
(x+4)(x+5)
Q4ApplicationModerateClass 8
3x²+6x?
View Solution
3x(x+2)
Final Chapter Summary
Chapter Summary
- Factorisation writes an expression as a product.
- Look for a common factor first.
- Regrouping can create a common binomial factor.
- Difference of squares factors as (a+b)(a-b).
- Multiplication is the best check of a factorisation.
- Prioritise correct method, clean working and final units where applicable.