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Expanding a bracket feels mechanical. Going the other way, from 49m² − 16 back to a product, feels like guessing until you see the pattern. Factorisation is that reverse step, and it is the same handful of identities you meet in Class 8, read from right to left. This post shows where the topic sits in the new NCERT books, gives three methods with worked examples, and ends with a short routine.
Is factorisation still in the Class 8 NCERT book?
The older NCERT book had a whole chapter on it, Chapter 12, Factorisation, according to its contents page. The new book is organised differently:
Ganita Prakash Part I, Chapter 6, "We Distribute, Yet Things Multiply", teaches the distributive property and these identities: (a + m)(b + n) = ab + mb + an + mn, (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², and (a + b)(a − b) = a² − b².
The word "factorisation" does not appear in the new Class 8 chapters. Factorisation by name is in the new Class 9 book, Ganita Manjari Part I (first edition April 2026), in Chapter 4, Exploring Algebraic Identities. Its sections include factorisation using identities and using algebra tiles.
So if your school uses the new Class 8 book, treat factorising as practice in reading your Class 8 identities backwards. It helps with mental arithmetic now and it is the opening move of algebra next year. Ask your teacher whether it will be tested this year.
What does it mean to factorise?
To factorise is to write an expression as a product of factors. Expanding 3xy(2x + 3y) gives 6x²y + 9xy². Factorising goes from 6x²y + 9xy² back to 3xy(2x + 3y).
Method 1: take out the common factor
Worked example 1. Factorise 6x²y + 9xy².
Numbers: the HCF of 6 and 9 is 3
Letters: both terms have at least one x and at least one y
Common factor: 3xy
Divide each term by it: 6x²y ÷ 3xy = 2x, and 9xy² ÷ 3xy = 3y
Answer: 3xy(2x + 3y)
Check: 3xy × 2x = 6x²y and 3xy × 3y = 9xy²
Worked example 2. Factorise 4a + 4. The answer is 4(a + 1). The 1 matters: 4 ÷ 4 = 1, and without it the bracket would expand to 4a only.
Method 2: use an identity backwards
Worked example 3. Factorise 49m² − 16.
Spot two squares with a minus between them: 49m² = (7m)² and 16 = 4²
Use a² − b² = (a + b)(a − b)
Answer: (7m + 4)(7m − 4)
Check: 49m² − 28m + 28m − 16 = 49m² − 16
Worked example 4. Factorise 9p² − 30p + 25.
First and last terms are squares: 9p² = (3p)² and 25 = 5²
Middle term: 2 × 3p × 5 = 30p, with a minus sign
So it matches (a − b)² = a² − 2ab + b²
Answer: (3p − 5)²
Worked example 5. Factorise 2x² − 8.
Common factor first: 2(x² − 4)
Then the identity: 2(x + 2)(x − 2)
Stopping at 2(x² − 4) is a common way to lose a mark
Method 3: grouping
Worked example 6. Factorise xy + 3x + 2y + 6.
Group in pairs: x(y + 3) + 2(y + 3)
(y + 3) is now a common factor: (x + 2)(y + 3)
Check by expanding: xy + 3x + 2y + 6
This is the book's first identity, (a + m)(b + n), read backwards.
Where does factorisation help in arithmetic?
The Class 8 chapter uses identities to calculate, and factorisation makes this quick.
47 × 53 = (50 − 3)(50 + 3) = 50² − 3² = 2500 − 9 = 2491
87² − 13² = (87 + 13)(87 − 13) = 100 × 74 = 7400
Which mistakes come up most often?
Dropping the 1. 4a + 4 is 4(a + 1), not 4a.
Not factorising fully. Look inside every bracket for another common factor or a difference of squares.
Treating a² + b² as (a + b)². With a = 3 and b = 4, a² + b² = 25 but (a + b)² = 49.
Sign slips in (a − b)². The middle term is −2ab, and the last term is +b².
Missing a hidden square. 16, 25, 49 and 9p² are squares; 18 and 12 are not.
How should you practise factorisation?
Start with worked examples, not a blank page. In a series of experiments, Sweller and Cooper (1985) found that studying worked examples of algebra took students much less time than solving the same problems conventionally, and that they then solved similar problems faster and with fewer errors.
Day 1: Study worked examples 1 to 6 above. Cover each, redo it, and compare.
Day 2: Alternate: one worked example, then one similar problem of your own.
Day 3: Take ten mixed expressions. For each, first write the method (common factor, identity or grouping), then factorise.
Day 4: Expand every answer from Day 3 to check it, and log any slips by type.
Day 5: Use identities for five mental calculations like 47 × 53.
The identities themselves are covered in our guide to algebraic expressions and identities in Class 8. When a factorisation will not come out, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
Try this now: factorise 25y² − 36 and 3a² + 6ab, then expand both answers to check.
