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**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, 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.

**Also Check: Rational Number Worksheet**

### CBSE Class 8 Maths Factorisation Worksheet PDF

CBSE Class 8 Maths Factorisation Worksheets provides study materials designed to help Class 8 students strengthen their grasp of factorisation concepts in Mathematics.. This printable PDF worksheet is aligned with the latest CBSE syllabus, ensuring it meets academic standards. The worksheets include different ways to factor numbers. They start with easy questions and go up to harder ones. The instructions are clear, and there are lots of exercises to practice. After each exercise, there are answers to check how well you did. By using these worksheets often, students can help themselves learn better. They can review important ideas and get ready for tests.

Refer: **Download Class 8 Factorisation Problems PDF**

### Class 8 Maths Factorisation Worksheet Questions with Answers

**Q1. Factorise the following expressions.
**(a) 54m

^{3}n + 81m

^{4}n

^{2}

(b) 15x

^{2}y

^{3}z + 25x

^{3}y

^{2}z + 35x

^{2}y

^{2}z

^{2}

Solution:

(a) 54m

^{3}n + 81m

^{4}n

^{2}

= 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)

= 27m

^{3}n (2 + 3mn)

(b) 15x^{2}y^{3}z + 25 x^{3}y^{2}z + 35x^{2}y^{2}z^{2} = 5x^{2}y^{2}z ( 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) p^{2}q – pr^{2} – pq + r^{2}

(b) x^{2} + yz + xy + xz

Solution:

(a) p^{2}q – pr^{2} – pq + r^{2}

= (p^{2}q – pq) + (-pr^{2} + r2)

= pq(p – 1) – r^{2}(p – 1)

= (p – 1) (pq – r^{2})

(b) x^{2} + yz + xy + xz

= x^{2} + xy +xz + yz

= x(x + y) + z(x + y)

= (x + y) (x + z)

**Q4. Factorise the following polynomials.**

(a) xy(z^{2} + 1) + z(x^{2} + y^{2})

(b) 2axy^{2} + 10x + 3ay^{2} + 15

Solution:

(a) xy(z^{2} + 1) + z(x^{2} + y^{2})

= xyz^{2} + xy + 2x^{2} + zy^{2}

= (xyz^{2} + zx^{2}) + (xy + zy^{2})

= zx(yz + x) + y(x + yz)

= zx(x + yz) + y(x + yz)

= (x + yz) (zx + y)

(b) 2axy^{2} + 10x + 3ay^{2} + 15

= (2axy^{2} + 3ay^{2}) + (10x + 15)

= ay^{2}(2x + 3) +5(2x + 3)

= (2x + 3) (ay^{2} + 5)

**Q5. Factorise the following expressions.**

(а) x^{2} + 4x + 8y + 4xy + 4y^{2}

(b) 4p^{2} + 2q^{2} + p^{2}q^{2} + 8

Solution:

(a) x^{2} + 4x + 8y + 4xy + 4y^{2}

= (x^{2} + 4xy + 4y^{2}) + (4x + 8y)

= (x + 2y)^{2} + 4(x + 2y)

= (x + 2y)(x + 2y + 4)

(b) 4p^{2} + 2q^{2} + p^{2}q^{2} + 8

= (4p^{2} + 8) + (p^{2}q^{2} + 2q^{2})

= 4(p^{2} + 2) + q^{2}(p^{2} + 2)

= (p^{2} + 2)(4 + q^{2})

**Q6. Factorise:**

(a) a^{2} + 14a + 48

(b) m^{2} – 10m – 56

Solution:

(a) a^{2} + 14a + 48

= a^{2} + 6a + 8a + 48

[6 + 8 = 14 ; 6 × 8 = 48]
= a(a + 6) + 8(a + 6)

= (a + 6) (a + 8)

(b) m^{2} – 10m – 56

= m^{2} – 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) 16x^{4} – 81

(b) (a – b)^{2} + 4ab

Solution:

(a) 16x^{4} – 81

= (4x^{2})^{2} – (9)2

= (4x^{2} + 9)(4x^{2} – 9)

= (4x^{2} + 9)[(2x)^{2} – (3)^{2}]
= (4x^{2} + 9)(2x + 3) (2x – 3)

(b) (a – b)^{2} + 4ab

= a^{2} – 2ab + b^{2} + 4ab

= a^{2} + 2ab + b^{2}

= (a + b)^{2}

**Don’t Miss:**

**Factorisation Class 8 Notes****NCERT Solutions Class 8 Factorisation****RD Sharma Class 8 Factorisation Solutions**

## CBSE Class 8 Maths Factorisation Worksheet FAQs

### What types of questions are typically found in the Class 8 Factorisation Worksheet PDF?

The Class 8 Factorisation Worksheet PDF usually contains a variety of questions covering topics such as factorising algebraic expressions, factorising quadratic expressions, identifying common factors, solving factorisation-related word problems, and factorising polynomials.

### How can Class 8 students enhance their speed and accuracy in mathematics?

Class 8 students can improve their speed and accuracy in mathematics by engaging in regular practice, comprehensively understanding mathematical concepts, utilizing shortcuts and strategies where applicable, solving previous years' question papers, seeking assistance from teachers or tutors as needed, and maintaining a positive attitude towards learning and problem-solving.

### What are some common errors students should avoid when factorising expressions in Class 8?

Common mistakes to avoid when factorising expressions in Class 8 include neglecting to check for common factors, improperly applying factorisation methods, misinterpreting given expressions, making computational errors, and overlooking negative signs or coefficients.

### How significant is factorisation within the CBSE Class 8 Maths curriculum?

Factorisation holds substantial importance within the CBSE Class 8 Maths syllabus as it serves as a foundational concept for comprehending higher-level algebraic concepts and problem-solving techniques.