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

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

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.

Q1. Factorise: $36a^2 + 12abc - 15b^2c^2$

Q2. Factorise: $15x^2 - 16xy^2 - 15y^2z^2$

Q3. Factorise: $p^2q - pr^2 - pq + r^2$

Q4. Factorise: $x^2 + xy + xz + yz$

Q5. Factorise: $axy + bcy - axz - bcz$

Q6. Factorise: $lm^2 - mn^2 - lm + n^2$

Q7. Factorise: $6xy + 6 - 9y - 4x$

Q8. Factorise: $3x - 2x^2y + 3xy^2 - 6y^3$

Q9. Factorise: $abx^2 + (ay - b)x - y$

Q10. Factorise: $x^2 - 11xy - x + 11y$

*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.*

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.

Q11. Factorise: $(x - 2y)^2 - 5(x - 2y) + 6$

Q12. Factorise: $(2a - b)^2 + 2(2a - b) - 8$

Q13. Factorise: $(ax + by)^2 + (bx - ay)^2$

Q14. Factorise: $ab(x^2 + 1) + x(a^2 + b^2)$

Q15. Factorise: $a^2x^2 + (ax^2 + 1)(x + a)$

Q16. Factorise: $16x^2 - 25y^2$

Q17. Factorise: $144a^2 - 289b^2$

Q18. Factorise: $(2x + 2y)^2 - 4(2x - y)^2$

Q19. Factorise: $a^4 + 1 - 2a^2$

Q20. Factorise: $x^4 - 4x^2 - 5$

*Tip: For Q11 and Q12, let $t = (x - 2y)$ or $t = (2a - b)$. The expression becomes a simple quadratic in $t$. For Q16–Q18, use $a^2 - b^2 = (a+b)(a-b)$.*

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.

Q21. Factorise: $81c^4 - (m + n)^2$

Q22. Factorise: $1 - \frac{1}{a^4}$

Q23. Factorise: $75a^3 - 108ab^4$

Q24. Factorise: $256x^8 - 81y^4$

Q25. Factorise: $(2b + c)^4 - (2b + c)^2$

Q26. Factorise: $3x^3y - 243xy^3$

Q27. Factorise: $(3x + 4y)^4 - x^4$

Q28. Factorise: $x^4 - 2x^2y + 1$

Q29. Factorise: $a^4 - 81c^4$

Q30. Factorise: $(a^2 - 5a)^2 - 36$

*Tip: For expressions like $a^4 - b^4$, apply difference of squares twice: first as $(a^2)^2 - (b^2)^2 = (a^2 + b^2)(a^2 - b^2)$, then factorise $a^2 - b^2$ again. Always check if you can factorise further!*

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.

Q31. Factorise: $a^2 + 2ab + b^2 - 16$

Q32. Factorise: $9a^4 - 24a^2b^2 + 16b^4 - 256$

Q33. Factorise: $a^2 - 2ab + b^2 - c^2$

Q34. Factorise: $25 - p^2 - q^2 - 2pq$

Q35. Factorise: $49 - a^2 + 8ab - 16b^2$

Q36. Factorise: $25x^2 - 10x + 1 - 36y^2$

Q37. Factorise: $a^2 - b^2 + 2bc - c^2$

Q38. Factorise: $a^2 + 4b^2 - 4ab - 4c^2$

Q39. Factorise: $(xy + 1)^2 - (x - y)^2$

Q40. Factorise: $49(a - b)^2 - 25(a + b)^2$

*Tip: The key pattern here is to first form a perfect square from some terms, e.g. $a^2 + 2ab + b^2 = (a+b)^2$, then apply $A^2 - B^2 = (A+B)(A-B)$ on the result. Rearranging before factorising is crucial.*

How to Use These Questions Effectively

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

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