How many questions on factorisation come in CBSE Class 8 exams?

Typically 2–3 questions worth 6–10 marks appear from Chapter 14 (Factorisation) in CBSE Class 8 exams. These can range from simple common-factor extraction to identity-based and regrouping problems. Practising a variety ensures you're ready for any combination.

What are the most important algebraic identities for factorisation?

The four key identities for Class 8 factorisation are: (1) $(a+b)^2 = a^2 + 2ab + b^2$, (2) $(a-b)^2 = a^2 - 2ab + b^2$, (3) $a^2 - b^2 = (a+b)(a-b)$, and (4) $(x+a)(x+b) = x^2 + (a+b)x + ab$. Most exam questions can be solved using these four.

How do I know which factorisation method to use?

Start by checking for a common factor across all terms. If there's none, look for an identity pattern (perfect square, difference of squares). If neither works, try regrouping terms into pairs. For trinomials, splitting the middle term is usually the way to go. With practice, identifying the right method becomes almost instinctive.

Is factorisation important for Class 9 and 10?

Absolutely. Factorisation is foundational for polynomials (Class 9), quadratic equations (Class 10), and algebraic fractions. Students who master it in Class 8 consistently perform better in higher classes because they can simplify expressions quickly and accurately.

Can I use these questions for ICSE Class 8 as well?

Yes! The factorisation methods and question types are the same across CBSE and ICSE for Class 8. ICSE may occasionally include slightly harder variations, which is exactly why we've included challenging questions in Sections C and D.

How many questions on factorisation come in CBSE Class 8 exams?

Typically 2–3 questions worth 6–10 marks appear from Chapter 14 (Factorisation) in CBSE Class 8 exams. These can range from simple common-factor extraction to identity-based and regrouping problems. Practising a variety ensures you're ready for any combination.

What are the most important algebraic identities for factorisation?

The four key identities for Class 8 factorisation are: (1) $(a+b)^2 = a^2 + 2ab + b^2$, (2) $(a-b)^2 = a^2 - 2ab + b^2$, (3) $a^2 - b^2 = (a+b)(a-b)$, and (4) $(x+a)(x+b) = x^2 + (a+b)x + ab$. Most exam questions can be solved using these four.

How do I know which factorisation method to use?

Start by checking for a common factor across all terms. If there's none, look for an identity pattern (perfect square, difference of squares). If neither works, try regrouping terms into pairs. For trinomials, splitting the middle term is usually the way to go. With practice, identifying the right method becomes almost instinctive.

Is factorisation important for Class 9 and 10?

Absolutely. Factorisation is foundational for polynomials (Class 9), quadratic equations (Class 10), and algebraic fractions. Students who master it in Class 8 consistently perform better in higher classes because they can simplify expressions quickly and accurately.

Can I use these questions for ICSE Class 8 as well?

Yes! The factorisation methods and question types are the same across CBSE and ICSE for Class 8. ICSE may occasionally include slightly harder variations, which is exactly why we've included challenging questions in Sections C and D.

Solved Examples

Top 40 CBSE Class 8 Factorisation Questions to Get a Perfect Score

Master every factorisation method — common factors, regrouping, identities, and difference of squares — with these handpicked practice questions.

CBSEICSEClass 8

The SparkEd Authors (IITian & Googler)6 March 202612 min read

Why Factorisation Is a Make-or-Break Chapter

$Factorisation is one of those chapters that separates students who breeze through algebra from those who struggle with it for years. In CBSE Class 8 (Chapter 14), you learn four core methods, and every single one of them shows up again in Class 9, Class 10, and beyond.$

$The problem? Most students only practice the easy textbook examples and then get blindsided by twisted questions in exams. That's why we've put together 40 carefully chosen questions that cover every method and difficulty level. If you can solve all 40, you're not just ready for your Class 8 exam. You're building a foundation that will carry you through board exams.$

$Grab a notebook, show your steps clearly, and let's get started.$

The 4 Methods You Must Know

$Before jumping into the questions, make sure you're comfortable with these four factorisation techniques:$

$3x^2 + 6x = 3x(x + 2)$

$ax + ay + bx + by = a(x+y) + b(x+y) = (a+b)(x+y)$

$a^2 - b^2$

$x^2 + bx + c$

$Every question below uses one or more of these methods. Try to identify the method before you start solving. That alone is half the battle.$

Section A: Common Factor & Basic Regrouping (Questions 1–10)

$These questions test your ability to spot common factors and regroup terms. Start here to build confidence.$

$36a^2 + 12abc - 15b^2c^2$

$15x^2 - 16xy^2 - 15y^2z^2$

$p^2q - pr^2 - pq + r^2$

$x^2 + xy + xz + yz$

$axy + bcy - axz - bcz$

$lm^2 - mn^2 - lm + n^2$

$6xy + 6 - 9y - 4x$

$3x - 2x^2y + 3xy^2 - 6y^3$

$abx^2 + (ay - b)x - y$

$x^2 - 11xy - x + 11y$

$Tip: For Q3-Q10, try rearranging the terms into two groups of two. The common factor from each group should give you a shared bracket.$

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Section B: Algebraic Identities & Substitution (Questions 11–20)

$These questions require you to recognise and apply algebraic identities. Some involve substitution — treat a bracket as a single variable.$

$(x - 2y)^2 - 5(x - 2y) + 6$

$(2a - b)^2 + 2(2a - b) - 8$

$(ax + by)^2 + (bx - ay)^2$

$ab(x^2 + 1) + x(a^2 + b^2)$

$a^2x^2 + (ax^2 + 1)(x + a)$

$16x^2 - 25y^2$

$144a^2 - 289b^2$

$(2x + 2y)^2 - 4(2x - y)^2$

$a^4 + 1 - 2a^2$

$x^4 - 4x^2 - 5$

$t = (x - 2y)$

Section C: Difference of Squares & Higher Powers (Questions 21–30)

$Now we step it up. These involve nested identities, fourth powers, and expressions that need multiple rounds of factorisation.$

$81c^4 - (m + n)^2$

$1 - \frac{1}{a^4}$

$75a^3 - 108ab^4$

$256x^8 - 81y^4$

$(2b + c)^4 - (2b + c)^2$

$3x^3y - 243xy^3$

$(3x + 4y)^4 - x^4$

$x^4 - 2x^2y + 1$

$a^4 - 81c^4$

$(a^2 - 5a)^2 - 36$

$a^4 - b^4$

Section D: Mixed & Exam-Level Challenges (Questions 31–40)

$These are the questions that separate toppers from the rest. They combine multiple methods and require careful rearrangement.$

$a^2 + 2ab + b^2 - 16$

$9a^4 - 24a^2b^2 + 16b^4 - 256$

$a^2 - 2ab + b^2 - c^2$

$25 - p^2 - q^2 - 2pq$

$49 - a^2 + 8ab - 16b^2$

$25x^2 - 10x + 1 - 36y^2$

$a^2 - b^2 + 2bc - c^2$

$a^2 + 4b^2 - 4ab - 4c^2$

$(xy + 1)^2 - (x - y)^2$

$49(a - b)^2 - 25(a + b)^2$

$a^2 + 2ab + b^2 = (a+b)^2$

How to Use These Questions Effectively

$Don't just read through the questions. Actually solve them. Here's a study plan that works:$

$On Day 1, solve Section A (Q1 to 10) and focus on writing every step clearly. On Day 2, tackle Section B (Q11 to 20). If you get stuck on identity based questions, revise algebraic identities first. Day 3 is for Section C (Q21 to 30). Time yourself and aim for 3 to 4 minutes per question. Day 4 covers Section D (Q31 to 40). These are exam level, so don't worry if they take longer. On Day 5, redo any questions you got wrong or couldn't complete.$

$If you can solve all 40 without looking at hints, you're in excellent shape for any factorisation question your exam throws at you.$

Common Mistakes to Avoid

$a^2 - b^2$

The SparkEd Advantage

$At SparkEd, every factorisation question comes with visual step by step solutions that show you exactly how each expression is broken down. You get three difficulty levels (Easy, Medium, Hard) so you always practise at the right challenge level.$

$When you're stuck, Super Power Help gives you a hint instead of jumping straight to the answer. And if you need more guidance, Spark the Coach is an AI tutor that asks guiding questions to help you figure out the method yourself.$

$These 40 questions are a great start, but if you want unlimited practice with instant feedback, try our Class 8 Factorisation topic for free.$

Written by the SparkEd Math Team

$Built by an IITian and a Googler. Trusted by parents from Google, Microsoft, Meta, McKinsey and more.$

$Serving Classes 6 to 10 across CBSE, ICSE, IB MYP and Olympiad.$

$www.sparkedmaths.com | info@sparkedmaths.com$

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