Factorisation Worksheet Class 8 Maths

Factorisation Class 8 Worksheets: Explore and download the free PDF version of CBSE Factorisation worksheet for Class 8 Maths. Our CBSE Class 8 Maths Factorisation Worksheets are carefully designed to match the latest syllabus and exam format set by CBSE. These worksheets aim to assist students in understanding the concept of factorisation more easily. You can access Class 8 Maths worksheets for each chapter along with detailed answers to improve your Maths skills and proficiency.

Factorisation Worksheet Class 8 Maths

Factorisation is a important mathematical concept, especially in algebra, essential for simplifying expressions and solving equations. In CBSE Class 8 Maths Syllabus, the Factorisation chapter teaches students to express algebraic expressions as products of their factors. By breaking down complex expressions into simpler factors, students can solve problems efficiently and understand algebraic manipulation better. This chapter covers several techniques for factorising algebraic expressions. These techniques include common factorisation, factorisation by grouping, and special factorisation formulas such as perfect squares and cubes. Mastery of factorisation not only aids in solving mathematical problems but also forms the basis for advanced topics in algebra and calculus.

Class 8 Maths Factorisation Worksheet Questions with Answers

Q1. Factorise the following expressions.
(a) 54m³n + 81m⁴n²
(b) 15x²y³z + 25x³y²z + 35x²y²z²
Solution:
(a) 54m³n + 81m⁴n²
= 2 × 3 × 3 × 3 × m × m × m × n + 3 × 3 × 3 × 3 × m × m × m × m × n × n
= 3 × 3 × 3 × m × m × m × n × (2 + 3 mn)
= 27m³n (2 + 3mn)

(b) 15x²y³z + 25 x³y²z + 35x²y²z² = 5x²y²z ( 3y + 5x + 7)

Q2. Factorise the following polynomials.
(a) 6p(p – 3) + 1 (p – 3)
(b) 14(3y – 5z)³ + 7(3y – 5z)²
Solution:
(a) 6p(p – 3) + 1 (p – 3) = (p – 3) (6p + 1)
(b) 14(3y – 5z)³ + 7(3y – 5z)²
= 7(3y – 5z)² [2(3y – 5z) +1]
= 7(3y – 5z)² (6y – 10z + 1)

Q3. Factorise the following:
(a) p²q – pr² – pq + r²
(b) x² + yz + xy + xz
Solution:
(a) p²q – pr² – pq + r²
= (p²q – pq) + (-pr² + r2)
= pq(p – 1) – r²(p – 1)
= (p – 1) (pq – r²)

(b) x² + yz + xy + xz
= x² + xy +xz + yz
= x(x + y) + z(x + y)
= (x + y) (x + z)

Q4. Factorise the following polynomials.
(a) xy(z² + 1) + z(x² + y²)
(b) 2axy² + 10x + 3ay² + 15
Solution:
(a) xy(z² + 1) + z(x² + y²)
= xyz² + xy + 2x² + zy²
= (xyz² + zx²) + (xy + zy²)
= zx(yz + x) + y(x + yz)
= zx(x + yz) + y(x + yz)
= (x + yz) (zx + y)

(b) 2axy² + 10x + 3ay² + 15
= (2axy² + 3ay²) + (10x + 15)
= ay²(2x + 3) +5(2x + 3)
= (2x + 3) (ay² + 5)

Q5. Factorise the following expressions.
(а) x² + 4x + 8y + 4xy + 4y²
(b) 4p² + 2q² + p²q² + 8
Solution:
(a) x² + 4x + 8y + 4xy + 4y²
= (x² + 4xy + 4y²) + (4x + 8y)
= (x + 2y)² + 4(x + 2y)
= (x + 2y)(x + 2y + 4)

(b) 4p² + 2q² + p²q² + 8
= (4p² + 8) + (p²q² + 2q²)
= 4(p² + 2) + q²(p² + 2)
= (p² + 2)(4 + q²)

Q6. Factorise:
(a) a² + 14a + 48
(b) m² – 10m – 56
Solution:
(a) a² + 14a + 48
= a² + 6a + 8a + 48
[6 + 8 = 14 ; 6 × 8 = 48]
= a(a + 6) + 8(a + 6)
= (a + 6) (a + 8)

(b) m² – 10m – 56
= m² – 14m + 4m – 56
[14 – 4 = 10; 4 × 4 = 56]
= m(m – 14) + 6(m – 14)
= (m – 14) (m + 6)

Q7. Factorise the following polynomials.
(a) 16x⁴ – 81
(b) (a – b)² + 4ab
Solution:
(a) 16x⁴ – 81
= (4x²)² – (9)2
= (4x² + 9)(4x² – 9)
= (4x² + 9)[(2x)² – (3)²]
= (4x² + 9)(2x + 3) (2x – 3)

(b) (a – b)² + 4ab
= a² – 2ab + b² + 4ab
= a² + 2ab + b²
= (a + b)²

Section A: 1-Mark Questions (Very Short Answer)

(Simple common factor questions, 5 × 1 = 5 marks)

Q1. Factorise: 12x + 20
Answer: 4(3x + 5)

Q2. Factorise: 15a²b + 25ab²
Answer: 5ab(3a + 5b)

Q3. Factorise: 7p² – 14p
Answer: 7p(p – 2)

Q4. Factorise: 9x³ – 3x²
Answer: 3x²(3x – 1)

Q5. Factorise: 16y² – 4y
Answer: 4y(4y – 1)

Section B: 2-Mark Questions (Short Answer Type)

(Simple regrouping and identity-based, 5 × 2 = 10 marks)

Q6. Factorise: 15pq + 15 + 9q + 25p
Answer:
= (15pq + 15) + (9q + 25p)
= 15(qp + 1) + (9q + 25p)
= (qp + 1)(15 + 9) [after regrouping appropriately]

Q7. Factorise using identity: 49p² – 36
Answer: = (7p)² – (6)² = (7p + 6)(7p – 6)

Q8. Factorise: x² + 10x + 25
Answer: = (x + 5)²

Q9. Factorise: a² – 121
Answer: = (a + 11)(a – 11)

Q10. Factorise: 4x² – 25y²
Answer: = (2x + 5y)(2x – 5y)

Section C: 3-Mark Questions (Application Based)

(Division of polynomials and multi-step problems, 5 × 3 = 15 marks)

Q11. Divide: (12x³ + 18x²) ÷ 6x
Answer: = (12x³ ÷ 6x) + (18x² ÷ 6x) = 2x² + 3x

Q12. Divide: (20m²n – 30mn²) ÷ 10mn
Answer: = 2m – 3n

Q13. Divide: (28x⁴ – 56x³) ÷ 14x²
Answer: = (28x⁴ ÷ 14x²) – (56x³ ÷ 14x²) = 2x² – 4x

Q14. Factorise: 25x² – 30xy + 9y²
Answer: = (5x – 3y)²

Q15. Factorise: p³ + q³
Answer: = (p + q)(p² – pq + q²)

Section D: 4-Mark Questions (Long Answer / Higher Order Thinking)

(Hard questions and word problems, 5 × 4 = 20 marks)

Q16. The area of a rectangle is given as (x² + 7x + 12). If its width is (x + 3), find its length.
Answer:
Length = (x² + 7x + 12) ÷ (x + 3)
= (x + 3)(x + 4) ÷ (x + 3)
= (x + 4)

Q17. Factorise: ab + bc + ca + a² + b² + c²
Answer: = (a + b + c)²

Q18. Factorise: x³ – 27
Answer: = (x – 3)(x² + 3x + 9)

Q19. If the area of a square is given by the expression (x² – 14x + 49), find the side of the square.
Answer:
Area = (x² – 14x + 49)
= (x – 7)²
∴ Side = (x – 7)

Q20. A rectangular park has an area given by (y² – 16). If its length is (y + 4), find its breadth.
Answer:
Breadth = (y² – 16) ÷ (y + 4)
= (y + 4)(y – 4) ÷ (y + 4)
= (y – 4)

Marking Scheme Alignment (as per CBSE Class 8 Maths pattern)

• 1-mark questions (simple factorisation): 5 questions = 5 marks
• 2-mark questions (identities, regrouping): 5 questions = 10 marks
• 3-mark questions (division + medium difficulty): 5 questions = 15 marks
• 4-mark questions (HOTs/word problems): 5 questions = 20 marks

Total: 20 questions = 50 marks

This makes the worksheet balanced, exam-aligned, and suitable for both practice and assessment.

What Makes Our Factorisation Worksheet Special?

• Perfectly Aligned with Your Syllabus: Our worksheets are carefully designed to match the latest CBSE syllabus, so you practice exactly what you need for your exams.
• Covers Every Important Topic: From finding common factors and grouping terms to using key algebraic identities, every concept from the chapter is included.
• Step-by-Step Difficulty: The questions start easy and gradually become more challenging, helping you build a strong foundation and confidence.
• Includes Detailed Answers: You don't have to guess if you're right. A complete answer key is provided to help you check your solutions and understand the correct method.
• Free Printable PDF: Easily download and print the CBSE Class 8 Maths Factorisation Worksheet PDF to study anytime, anywhere.