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MathematicsClass 8Factorisation

Factorisation | Class 8 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 5 min read

Factorisation – this guide gives you a concise, exam-ready overview of Factorisation from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

How to Factorise?

This section explains the various methods to factorise algebraic expressions. The primary method introduced is taking out the common factors from the terms of the expression. When all terms have a common factor, it can be taken outside the bracket, leaving the remaining terms inside. For example, in 12x + 18, both terms are divisible by 6, so 6 is taken out as a common factor, resulting in 6(2x + 3). Another method introduced is factorisation by grouping, where terms are grouped in pairs or sets, and common factors are taken out from each group, followed by taking out the common binomial factor. The section also introduces special products such as the difference of squares, where expressions like a² - b² can be factorised as (a - b)(a + b). The section provides step-by-step procedures and examples to illustrate these methods. Understanding these methods is essential for factorising more complex expressions and solving algebraic equations.

📊 Diagram: Diagrams illustrating factorisation by taking common factors and by grouping terms, showing the stepwise extraction of common factors.

🧪 Activity: Activity to factorise given expressions by taking common factors and by grouping.

🔗 Connection: Leads to the next section 'Factorisation of Algebraic Expressions' which covers specific types of expressions and their factorisation.

Frequently asked questions

1. Find the common factors of the given terms. (i) 12x, 36 (ii) 2y, 22xy (iii) 14 pq, 28 p^2 q^2 (iv) 2x, 3x^2, 4 (v) 6 abc, 24 ab^2, 12 a^2 b (vi) 16 x^3, -4 x^2, 32 x (vii) 10 pq, 20 qr, 30 rp (viii) 3 x^2 y^3, 10 x^3 y^2, 6 x^2 y^2 z

Solutions:

(i) 12x, 36 Common factors: Factors of 12x are 1,2,3,4,6,12,x; Factors of 36 are 1,2,3,4,6,9,12,18,36. Common factors: 1,2,3,4,6,12

(ii) 2y, 22xy Factors of 2y: 1,2,y Factors of 22xy: 1,2,11,x,y,22, etc. Common factors: 1,2,y

(iii) 14 pq, 28 p^2 q^2 Factors of 14 pq: 1,2,7,p,q Factors of 28 p^2 q^2: 1,2,4,7,14,p,p^2,q,q^2 Common factors: 1,2,7,p,q

(iv) 2x, 3x^2, 4 Factors of 2x: 1,2,x Factors of 3x^2: 1,3,x,x^2 Factors of 4: 1,2,4 Common factors: 1

(v) 6 abc, 24 ab^2, 12 a^2 b Fa

2. Factorise the following expressions. (i) 7x - 42 (ii) 6p - 12q (iii) 7a^2 + 14a (iv) -16z + 20z^3 (v) 20 l^2 m + 30 a l m (vi) 5 x^2 y - 15 x y^2 (vii) 10 a^2 - 15 b^2 + 20 c^2 (viii) -4 a^2 + 4 a b - 4 c a (ix) x^2 y z + x y^2 z + x y z^2 (x) a x^2 y + b x y^2 + c x y z

Solutions:

(i) 7x - 42 = 7(x - 6)

(ii) 6p - 12q = 6(p - 2q)

(iii) 7a^2 + 14a = 7a(a + 2)

(iv) -16z + 20z^3 = 4z(-4 + 5z^2) = 4z(5z^2 - 4)

(v) 20 l^2 m + 30 a l m = 10 l m (2 l + 3 a)

(vi) 5 x^2 y - 15 x y^2 = 5 x y (x - 3 y)

(vii) 10 a^2 - 15 b^2 + 20 c^2 = 5 (2 a^2 - 3 b^2 + 4 c^2)

(viii) -4 a^2 + 4 a b - 4 c a = -4 a^2 + 4 a b - 4 a c = -4 a (a - b + c)

(ix) x^2 y z + x y^2 z + x y z^2 = x y z (x + y + z)

(x) a x^2 y + b x y^2 + c x y z = x y (a x + b y + c z)

3. Factorise. (i) x^2 + x y + 8 x + 8 y (ii) 15 x y - 6 x + 5 y - 2 (iii) a x + b x - a y - b y (iv) 15 p q + 15 + 9 q + 25 p (v) z - 7 + 7 x y - x y z

Solutions:

(i) x^2 + x y + 8 x + 8 y = x(x + y) + 8(x + y) = (x + 8)(x + y)

(ii) 15 x y - 6 x + 5 y - 2 = 3 x (5 y - 2) + 1 (5 y - 2) = (3 x + 1)(5 y - 2)

(iii) a x + b x - a y - b y = x(a + b) - y(a + b) = (x - y)(a + b)

(iv) 15 p q + 15 + 9 q + 25 p = 15(p q + 1) + 9 q + 25 p = 15 p q + 15 + 9 q + 25 p Try grouping: = (15 p q + 9 q) + (25 p + 15) = 3 q (5 p + 3) + 5 (5 p + 3) = (3 q + 5)(5 p + 3)

(v) z - 7 + 7 x y - x y z = (z - x y z) + (7 x y - 7) = z(1 - x y) + 7(x y - 1) = z(1 - x y)

1. Factorise the following expressions. (i) a^2 + 8a + 16 (ii) p^2 - 10p + 25 (iii) 25m^2 + 30m + 9 (iv) 49y^2 + 84yz + 36z^2 (v) 4x^2 - 8x + 4 (vi) 121b^2 - 88bc + 16c^2 (vii) (l + m)^2 - 4lm (Hint: Expand (l + m)^2 first) (viii) a^4 + 2a^2b^2 + b^4

Solutions:

(i) a^2 + 8a + 16 = (a + 4)^2

(ii) p^2 - 10p + 25 = (p - 5)^2

(iii) 25m^2 + 30m + 9 = (5m + 3)^2

(iv) 49y^2 + 84yz + 36z^2 = (7y + 6z)^2

(v) 4x^2 - 8x + 4 = (2x - 2)^2

(vi) 121b^2 - 88bc + 16c^2 = (11b - 4c)^2

(vii) (l + m)^2 - 4lm = (l + m)^2 - (2√lm)^2 = (l + m - 2√lm)(l + m + 2√lm) But since 4lm = (2l)(2m), better to write: (l + m)^2 - 4lm = (l - m)^2

(viii) a^4 + 2a^2b^2 + b^4 = (a^2 + b^2)^2

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