Factorisation ICSE Class-8th Concise Selina Mathematics

Factorisation ICSE Class-8th Concise Selina Mathematics Solutions Chapter- 13. We provide step by step Solutions of Exercise / lesson-13 Factorisation for ICSE Class-8 Concise Selina Mathematics. Our Solutions contain all type Questions with Exe-13 A,  Exe-13 B, Exe-13 C, Exe-13 D, Exe-13 E  and Exe-13 F to develop skill and confidence . Visit official Website CISCE for detail information about ICSE Board Class-8.

Factorisation ICSE Class-8th Concise Selina Mathematics Solutions Chapter- 13


–: Select Topics :–

 

Exe-13 A,

Exe-13 B,

Exe-13 C,

Exe-13 D,

Exe-13 E,

Exe-13 F,

 


 Exercise – 13 A Factorisation Solved Questions for ICSE Class-8th Concise Selina Publications

 

Factorise :

Question 1 :-

15x + 5
Answer:

15x + 5

= 5(3x + 1)

Question 2 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-2
Answer

a3 – a2 +a

= a(a2 – a + 1)

Question 3 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-3
Answer

3x+ 6x3

= 3x(1 + 2x)

Question 4 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-4
Answer

4a2 – 8ab

= 4a (a – 2b)

Question 5 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-5
Answer

2x3b2 – 4x5b4

= 2x3b2 (1 – 2x2b2)

Question 6 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-6
Answer

15x4y3 – 20x3y

= 5x3y (3xy– 4)

Question 7 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-7
Answer

a3b – a2b2 – b3

= b(a3 – a2b – b2)

Question 8:-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-8
Answer

6x2y + 9xy2 + 4y3

= y (6x2 + 9xy + 4y2)

Question 9 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-9
Answer

17a6b8 – 34a4b6 + 51a2b4

= 17a2b4 (a4b4 – 2a2b2 + 3)

Question 10 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-10
Answer

3x5y – 27x4y2 + 12x3y

= 3x3y (x2 – 9xy + 4y2)

Question 11 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-11
Answer

x2(a-b)-y2 (a-b)+z2(a-b)

= (a – b)(x2 – y2 + z2)

Question 12 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-12
Answer

(x + y)(a + b) + (x – y)(a + b)

= (a+b) (x + y + x – y)

= (a + b) (2x)

= 2x (a + b)

Question 13 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-13
Answer

2b (2a + b) – 3c (2a + b)

= (2a + b) (2b – 3c)

Question 14 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-14
Answer

12abc – 6a2b2c2 + 3a3b3c3

= 3abc (4 – 2abc + a2b2c2)

Question 15 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-15
Answer

4x(3x – 2y) – 2y(3x – 2y)

= (3x – 2y) (4x – 2y)

= (3x – 2y) × 2(2x – y)

= 2(3x – 2y) (2x – y)

Question 16 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-16
Answer:

(a+ 2b) (3a + b) – (a+ b) (a+ 2b) +(a+ 2b)2

= (a + 2b) (3a + b – a – b + a + 2b)

= (a + 2b) (3a + 2b)

Question 17 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-A-17
Answer

6xy(a2 + b2) + 8yz(a2 + b2) -10xz(a2 + b2)

= H.C.F. of 6, 8, 10 = 2 , then

2(a2 + b2) (3xy + 4yz – 5xz)


Selina Concise Maths Factorisation of ICSE Class-8th Exercise – 13 B 

 

Question 1 :-

Factorise : a2 + ax + ab + bx
Answer :

a2 + ax + ab + bx

= (a2 + ax) + (ab + bx)

= a(a + x) + b (a + x)

= (a + x) (a + b)

Question 2 :-

Factorise : a2 – ab – ca + bc
Answer :

a2 – ab – ca + bc

= a(a – b) – c(a – b)

= (a – b) (a – c)

Question 3 :-

Factorise : ab – 2b + a2 – 2a
Answer

ab – 2b + a2 – 2a

= b(a – 2) + a(a – 2)

= (a – 2) (b + a)

Question 4:-

Factorise : a3 – a2 + a – 1
Answer

a3 -a2 +a -1

= a2 (a – 1) + 1 (a – 1)

= (a – 1) (a2 + 1)

Question 5 :-

Factorise : 2a – 4b – xa + 2bx
Answer

2a – 4b – xa + 2bx

= 2 (a – 2b) – x (a – 2b)

= (a – 2b) (2 – x)

Question 6 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-6
Answer

xy – ay – ax + a2 + bx – ab

= y (x – a) – a (x – a) + b (x – a)

= (x – a) (y – a + b)

Question 7 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-7
Answer

3x5 – 6x4 – 2x3 + 4x2 + x – 2

= 3x4 (x – 2) – 2x2 (x – 2) + 1 (x – 2)

= (x – 2) (3x4 – 2x2 + 1)

Question 8 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-8
Answer

– x2y – x + 3xy + 3

= 3 – x + 3xy – x2y

= 1(3 – x) + xy (3 – x)

= (3 – x) (1 + xy) = (xy + 1) (3 – x)

Question 9 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-9
Answer

6a2 – 3a2b – bc2 + 2c

= 6a2 – 3a2b + 2c2 – bc2

= 3a2 (2 – b) + c2 (2 – b)

= (2 – b) (3a2 + c2)

Question 10 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-10
Answer

3a2b – 12a2 – 9b + 36

= 3a2 (b – 4) – 9 (b – 4)

= (b – 4) (3a– 9) = (b – 4) 3 (a2 – 3)

= 3 (b – 4) (a-3)

Question 11 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-11
Answer

x2 – (a – 3)x – 3a

= x2 – ax + 3x – 3a

= x (x – a) + 3 (x – a)

= (x – a) (x + 3)

Question 12 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-12
Answer

x2 – (b – 2)x – 2b

= x2 – bx + 2x – 2b

= x (x – b) + 2(x – b)

= (x – b) (x + 2)

Question 13 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-13
Answer

a(b – c) – d(c – b)

= a (b – c) + d (b – c)

= (b – c) (a + d)

Question 14 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-14
Answer

ab2 – (a – c) b – c

= ab2 – ab + bc – c

= ab (b – 1) + c (b – 1)

= (b – 1) (ab + c)

Question 15 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-15
Answer

(a2 – b2) c + (b2 – c2)a

= a2c – b2c + ab2 – ac2

= a2c – ac2 + ab2 – b2c

= ac (a – c) + b2 (a – c)

= (a – c) (ac + b2)

Question 16 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-16
Answer

a3 – a2 – ab + a + b – 1

= a3 – a2 – ab + b + a – 1

= a2 (a – 1) – b (a – 1) + 1 (a – 1)

= (a – 1) (a2 – b + 1)

Question 17 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-17
Answer

ab(c2 + d2) – a2cd – b2cd

= abc2 + abd2 – a2cd – b2cd

= abc2 – a2cd – b2cd + abd2

= ac (bc – ad) – bd (bc – ad)

= (bc – ad) (ac – bd)

Question 18 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-18
Answer

2ab2 – aby + 2cby – cy2

= 2b (ab + cy) – y (ab + cy)

= (ab + cy) (2b – y)

Question 19 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-19
Answer

ax + 2bx + 3cx – 3a – 6b – 9c

= x (a + 2b + 3c) – 3 (a + 2b + 3c)

= (a + 2b + 3c) (x – 3)

Question 20 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-B-20
Answer

2ab2c – 2a + 3b3c – 3b – 4b2c2 + 4c

= 2a (b2c – 1) + 3b (b2c – 1) – 4c (b2c – 1)

= (b2c – 1) (2a + 3b – 4c)


Exercise – 13 C  Factorisation ICSE Class-8th Mathematics Solved

Question 1 :-

Factorise : 16 – 9x2
Answer

16 – 9x2

= (4)2 – (3x)2

= (4 + 3x) (4 – 3x)  …[a2 – b2 = (a + b) (a – b)]

Question 2 :-

Factorise : 1 – 100a2
Answer

1 – 100a2

= = (1)2 – (10a)2

= (1 + 10a) (1 – 10a)   …[a2 – b2 = (a + b) (a – b)]

Question 3 :-

Factorise : 4x2 – 81y2
Answer

4x2 – 81y

= (2x)2 – (9y)2

= (2x + 9y) (2x – 9y) …[a2 – b2 = (a + b) (a – b)]

Question 4 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-4
Answer

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation 41

Question 5 :-

Factorise : (a+2b)2 – a2
Answer

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation 42

Question 6 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-6
Answer

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation 43

Question 7 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-7
Answer:

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation 44

Question 8 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-8
Answer:

(5a – 2b)2 – (2a – b)2

= (5a – 2b + 2a – b) (5a – 2b – 2a + b)

= (7a – 3b) (3a – b)

Question 9 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-9
Answer:

1 – 25 (a+ b)2

= (1)2 – [5(a+b)]2

= [1 + 5(a+b)] [1 – 5(a+b)]

= (1 + 5a + 5b) (1 – 5a – 5b)

Question 10 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-10
Answer:

4(2a + b)2 – (a – b)2

= [2(2a + b)]2 – (a – b)2

= [2(2a + b) + a – b][2 (2a + b) -a + b]

= (4a + 2b + a – b)(4a + 2b – a + b)

= (5a + b)(3a + 3b)

= (5a + b) 3(a + b)

= 3 (5a + b) (a + b)

Question 11 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-11
Answer:

25(2x + y)2 – 16(x – y)2

= [5(2x + y)]2 – [4(x-y)]2

= (10x + 5y)2 – (4x – 4y)2

= (10x + 5y + 4x – 4y) (10x + 5y – 4x + 4y)

= (14x + y)(6x + 9y)

= (14x + y) 3(2x + 3y)

= 3 (14x + y)(2x + 3y)

Question 12 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-12
Answer:

49(x – y)2 -9(2x + y)2

= [7(x-y)]2 – [3(2x + y)]2

= (7x – 7y)2 – (6x + 3y)2

= (7x – 7y + 6x + 3y) (7x – 7y – 6x – 3y)

= (13x – 4y) (x – 10y)

Question 13 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-13
Answer:

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation 50

Question 14 :-

Evaluate :
selina-concise-mathematics-class-8-icse-solutions-factorisation-C-14
Answer

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation 51

Question 15 :-

Evaluate :
(0.7)2 – (0.3)2
Answer

(0·7)2 – (0·3)2

= (0.7 + 0.3) (0.7 – 0.3)  ….[a2 – b2 = (a + b) (a – b)]

= 1 × 0.4 = 0.4

Question 16 :-

Evaluate :
(4.5)2 – (1.5)2
Answer

(4.5)2 – (1.5)

= (4.5 + 1.5) (4.5 – 1.5) …[a2 – b2 = (a + b) (a – b)]

= 6 × 3 = 18

Question 17 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-17
Answer

75(x + y)2 – 48(x – y)2

= 3[25 (x + y)2 – 16 (x – y)2]

= 3[{5 (x + y)2} – {4 (x – y)}2]

Using a– b2 = (a + b) (a – b)

= 3 [5(x + y) + 4(x – y)] [5(x + y) – 4(x – y)]

= 3 [5x + 5y + 4x – 4y] [5x + 5y – 4x + 4y]

= 3 (9x + y) (x + 9y)

Question 18 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-18
Answer

a2 + 4a + 4 – b2

….[(a + b)2 = a2 + 2ab + b2]
….[a2 – b2 = (a + b)(a – b)]

= (a)2 + 2 × a × 2 + (2)2 – (b)2

= (a + 2)2 – (b)2

= (a + 2 + b) (a + 2 – b)

= (a + b + 2) (a – b + 2)

Question 19 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-19
Answer

a2 – b2 – 2b – 1

= a2 – (b2 + 2b + 1)

…[(a + b)2 = a2 + b2 + 2ab]
…[a2 – b2 = (a + b) (a – b)]

= (a)2 – (b + 1)2

= (a + b + 1)(a – b – 1)

Question 20 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-C-20
Answer

x2 + 6x + 9 – 4y

= (x)2 + 2 × x × 3 + (3)2 – (2y)2

…[(a + b)2 = a2 + 2ab + b2]
…[a2 – b2 = (a + b)(a – b)]

= (x + 3)2 – (2y)2

= (x + 3 + 2y) (x + 3 – 2y)

= (x + 2y + 3) (x – 2y + 3)


Selina Solutions Concise Mathematics Factorisation for ICSE Class-8th of Exercise – 13 D 

Question 1 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-1
Answer

x2 + 6x + 8

= x2 + 4x + 2x + 8

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

= (x+4) (x+2)

Question 2 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-2
Answer

x2 + 4x + 3

= x2 + 3x + x + 3

= x(x + 3) + 1 (x + 3)

= (x + 3) (x + 1)

Question 3 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-3
Answer

a2 +Sa+ 6

= a2 + 3a + 2a + 6

= a(a + 3) + 2(a + 3)

= (a + 3)(a + 2)

Question 4 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-4
Answer

a2 – 5a+ 6

= a2 – 3a – 2a + 6

= a(a – 3) – 2(a – 3)

= (a – 3)(a – 2)

Question5 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-5
Answer

a2 +5a – 6

= a2 + 6a – a – 6

= a (a + 6) – 1 (a + 6)

= (a + 6) (a – 1)

Question 6 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-6
Answer

x2 + 5xy + 4y2

= x2 + 4xy + xy + 4y2

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

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

Question 7 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-7
Answer

a2 – 3a- 40

= a2 – 8a + 5a – 40

= a(a – 8) + 5(a – 8)

= (a – 8)(a + 5)

Question 8 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-8
Answer

x2 – x – 72

= x2 – 9x + 8x – 72

= x(x – 9) + 8(x – 9)

= (x – 9)(x + 8)

Question 9 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-9
Answer

x2 – 10xy + 24y2

= x2 – 6xy – 4xy + 24y2

= x(x – 6y) – 4y(x – 6y)

= (x – 6y) (x – 4y)

Question 10 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-10
Answer

2a2 + 7a + 6

= 2a2 + 4a + 3a + 6

= 2a(a + 2) + 3(a + 2)

= (a + 2)(2a + 3)

Question 11 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-11
Answer

3a2 – 5a + 2

= 3a2 – 3a – 2a + 2

= 3a (a – 1) – 2(a – 1)

= (a – 1)(3a – 2)

Question 12 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-12
Answer

7b2 – 5b+ 1

= 7b2 – 7b – b +1

= 7b(b – 1) – 1(b – 1)

= (b – 1)(7b – 1)

Question 13 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-13
Answer

2a2 – 17ab + 26b2

= 2a2 – 13ab – 4ab + 26b2

= a(2a – 13b) – 2b(2a – 13b)

= (2a – 13b) (a – 2b)

Question 14 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-14
Answer

2x2 + xy – 6y2

= 2x2 + 4xy – 3xy – 6y2

= 2x (x + 2y) – 3y(x + 2y)

= (x + 2y)(2x – 3y)

Question 15 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-15
Answer

4c2 + 3c – 10

= 4c2 + 8c – 5c – 10

= 4c (c + 2) – 5(c + 2)

= (c + 2)(4c – 5)

Question 16 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-16
Answer

14x2 + x – 3

= 14x2 + 7x – 6x – 3

= 7x (2x + 1) – 3(2x + 1)

= (2x + 1) (7x – 3)

Question 17 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-17
Answer

6 + 7b – 3b2

= 6 + 9b – 2b – 3b2

= 3(2 + 3b) – b(2 + 3b)

= (2 + 3b)(3 – b)

Question 18 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-18
Answer

5 + 7x – 6x2

= 5 + 10x – 3x – 6x2

= 5(1 + 2x) – 3x(1 + 2x)

= (1 + 2x)(5 – 3x)

Question 19 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-19
Answer

4 + y – 14y2

= 4 + 8y – 7y – 14y2

= 4 (1 + 2y) – 7y (1 + 2y)

= (1 + 2y)(4 – 7y)

Question 20 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-20
Answer:

5 + 3a – 14a2

5 + 10a – 7a – 14a2

= 5(1 + 2a) – 7a (1 + 2a)

= (1 + 2a) (5 – 7a)

Question 21 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-21
Answer:

(2a + b)2 + 5(2a + b) + 6

Let (2a + b) = x

(2a + b)2 = x2

(2a + b)2 + 5 (2a + b) + 6

= x2 + 5x + 6

= x2 + 3x + 2x + 6

= x(x + 3)+2(x + 3)

= (x + 3)(x + 2)

= (2a + b + 3)(2a + b + 2)
(Substituting the value of x)

Question 22 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-22
Answer:

1 – (2x + 3y) – 6(2x + 3y)2

Let (2x + 3y) = a

∴ (2x + 3y)2 = a2

∴ 1 – (2x + 3y) – 6(2x + 3y)2

= 1 – a – 6a2

= 1 – 3a + 2a – 6a2

= 1(1 – 3a) + 2a (1 – 3a)

= (1 – 3a) (1 + 2a)

= [1 – 3 (2x + 3y)][1 + 2(2x + 3y)]
(Substituting the value of a)

= (1 – 6x – 9y) (1 + 4x + 6y)

Question 23 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-23
Answer:

(x – 2y)2 – 12(x – 2y) + 32

Let (x – 2y) = a

∴ (x – 2y)2 = a2

∴ (x – 2y)2 – 12(x – 2y) + 32

= a2 – 12a + 32

= a2 – 8a – 4a + 32

= a(a – 8) – 4 (a – 8)

= (a – 8)(a – 4)

= (x – 2y – 8)(x – 2y – 4)
(Substituting the value of a)

Question 24 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-24
Answer:

8 + 6(a + b) – 5(a + b)2

Let a + b = x

(a + b)2 = x2

8 + 6 (a+b) – 5(a + b)2

= 8 + 6x – 5x2

= 8 + 10x – 4x – 5x2

= 2(4 + 5x) – x (4 + 5x)

= (4 + 5x)(2 – x)

= [4 + 5(a + b)] [2 – (a + b)]

(Substituting the value of x)

= [4 + 5a + 5b][2 – a – b]

Question 25 :-

selina-concise-mathematics-class-8-icse-solutions-factorisation-D-25
Answer:

2(x + 2y)2 – 5(x + 2y) + 2

Let x + 2y = a, then

2a2 – 5a + 2

⇒ 2a2 – a – 4a + 2

= a(2a – 1) – 2(2a – 1)

= (2a – 1)(a – 2)

= {2(x + 2y – 1)} {(x + 2y) – 2}

= (2x + 4y – 2)(x + 2y – 2)
…[∵ 2 × 2 = 4]
[-5 = -1-4]
[4 = (-1) × (-4)]


Exe – 13 E of Factorisation for ICSE Class-8th Concise Mathematics Answer

 

Question 1 :-

In each case find whether the trinomial is a perfect square or not:
selina-concise-mathematics-class-8-icse-solutions-factorisation-E-1
Answer:

(i) 

x2 + 14x + 49

= (x)2 + 2 × x × 7 + (7)2

= (x + 7)2    …[a2 + 2ab + b=(a + b)2]

∴ The given trinomial x2 + 14x + 49 is a perfect square.

(ii)

a2 – 10a + 25

= (a)2 – 2 × a × 5 + (5)2

= (a – 5)  [∵ a2 – 2ab + b2 = (a – b)2]

∴ The given trinomial a2 – 10a + 25 is a perfect square.

(iii)

4x2 + 4x + 1

= (2x)2 + 2 × 2x × 1 + (1)2

=(2x + 1)2     [∵ a2 – 2ab + b2 = (a – b)2]

∴ The given trinomial 4x2 + 4x + 1 is a perfect square.

(iv)

9b2 + 12b + 16

= (3b)2 + 3b × 4 + (4)2

= x2 + xy + y2  …[Taking 3b = x, and 4 = y]

(v)

16x2 – 16xy + y

= (4x)2 – 4 ×4x × y + (y)2

= a2 – 4ab + b2

…[Taking 4x = a, and y = b]

∴ The given trinomial cannot be expressed as a2 + 2ab + b2 . Hence, it is not a perfect square.

(vi)

x2 – 4x + 16

= (x)2 – x × 4 + (4)2

= a – ab + b2

…[Taking x = a, and 4 = b]

∴ The given trinomial cannot be expressed as a2 – 2ab + b2. Hence, it is not a perfect square.

Question 2 :-

Factorise completely 2 – 8x2.
Answer:

2 – 8x2 = 2(1 – 4x2)

= 2[(1)2 – (2x)2]

= 2(1 + 2x) (1 – 2x)

Question 3 :-

Factorise completely : 8x2y – 18y3
Answer:

8x2y – 18y3 = 2y (4x2 – 9y2)

= 2y[(2x)2 – (3y)2]

= 2y (2x + 3y) (2x – 3y)

Question 4 :-

Factorise completely : ax2 – ay2
Answer:

ax2 – ay2 = a(x2 – y2)

= a (x + y)(x – y)

Question 5 :-

Factorise completely : 25x3 – x
Answer:

25x3 – x = x (25x2 – 1)

= x [(5x)2 – (1)2]

= x (5x + 1)(5x – 1)

Question 6 :-

Factorise completely : a4 – b4
Answer:

a4 – b4 = (a2)2 – (b2)2

= (a2 + b2) (a2 – b2)

= (a2 + b2)(a + b)(a – b)

Question 7 :-

Factorise completely : 16x4 – 81y4
Answer:

16x4 – 81y4  = (4x2)2 – (9y2)2

= (4x2 + 9y2) (4x2 – 9y2)

= (4x2 + 9y2)[(2x)2 – (3y)2]

= (4x2 + 9y2)(2x + 3y)(2x – 3y)

Question 8 :-

Factorise completely : 625 – x4
Answer:

625 – x4 = (25)2 – (x2)2

= (25 + x2) (25 – x2)

= (25 + x2) [(5)2 – (x)2]

= (25 + x2) (5 + x) (5 – x)

Question 9 :-

Factorise completely : x2 – y2 – 3x – 3y
Answer:

x2 – y2 – 3x – 3y = (x2 – y2) – 3 (x + y)

= (x + y) (x – y) – 3(x + y)

= (x + y)(x – y -3)

Question 10 :-

Factorise completely : x2 – y2 – 2x + 2y
Answer:

x2 – y2 – 2x + 2y = (x2 – y2) – 2(x – y)

= (x + y) (x – y) – 2(x – y)

= (x – y)(x + y – 2)

Question 11 :-

Factorise completely : 3x2 + 15x – 72
Answer

3x2 + 15x – 72 = 3 (x2 + 5x – 24)

= 3[x2 + 8x – 3x – 24]

= 3[x (x + 8) – 3 (x + 8)]

= 3[(x + 8)(x – 3)]

= 3 (x + 8)(x – 3)

Question 12 :-

Factorise completely : 2a2 – 8a – 64
Answer

2a2 – 8a – 64 = 2[a2 – 4a – 32]

= 2[a2 – 8a + 4a – 32]

= 2[a(a – 8) + 4(a – 8)]

= 2[(a – 8) (a + 4)]

= 2(a – 8)(a + 4)

Question 13 :-

Factorise completely : 5b2 + 45b + 90
Answer

 

Question 14 :-

Factorise completely : 3x2y + 11xy + 6y
Answer

5b2 + 45b + 90 = 5[b2 + 9b + 18]

= 5[b2 + 6b + 3b + 18]

= 5[b(b + 6) + 3(b + 6)]

= 5[(b + 6) (b + 3)]

= 5 (b + 6)(b + 3)

Question 15 :-

Factorise completely : 5ap2 + 11ap + 2a
Answer

5ap2 + 11ap + 2a = a[5p2 + 11p + 2]

= a[5p2 + 10p + p +2]

= a[5p(p+2) + 1(p + 2)]

= a[(p + 2)(5p + 1)]

= a (p + 2) (5p + 1)

Question 16 :-

Factorise completely : a2 + 2ab + b2 – c2
Answer

a2 + 2ab + b2 – c2
= (a2 + 2ab + b2) – c2

= (a + b)2 – (c)2

= (a + b+ c) (a + b – c)

Question 17 :-

Factorise completely : x2 + 6xy + 9y2 + x + 3y
Answer

x2 + 6xy + 9y2 + x + 3y

= [(x)2 + 2 × x × 3y + (3y)2] + (x + 3y)

= [x + 3y]2 + (x + 3y)

= (x + 3y) (x + 3y) + (x + 3y)

= (x + 3y) (x + 3y + 1)

Question 18 :-

Factorise completely : 4a2 – 12ab + 9b2 + 4a – 6b
Answer

4a2 -12ab + 9b2 + 4a- 6b

= [(2a)2 – 2 × 2a × 3b + (3b)2] + 2(2a – 3b)

= (2a – 3b)2 + 2(2a – 3b)

= (2a – 3b)(2a – 3b + 2)

Question 19 :-

Factorise completely : 2a2b2 – 98b4
Answer

2a2b2 – 98b4 = 2b2 (a2 – 49b2)

= 2b2 [(a)2 – (7b)2]

= 2b2 (a + 7b)(a – 7b)

Question 20 :-

Factorise completely : a2 – 16b2 – 2a – 8b
Answer

a2 -16b2 – 2a – 8b = [(a)4 – (4b)2] – 2(a + 4b)

= (a + 4b)(a – 4b) – 2(a + 4b)

= (a + 4b)(a – 4b – 2)


ICSE Class-8 Maths – Factorisation  Exercise – 13 F Selina Solutions

Question 1 :-

Factorise :
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-1
Answer

(i)

6x3 – 8x2

= 2x2 (3x – 4)

(ii) 

35a3b2c + 42ab2c2

= 7ab2c (5a2 + 6c)

(iii)

36x2y2 – 30x3y3 + 48x3y2

= 6x2y2 (6 – 5xy + 8xy)

(iv)

8(2a + 3b)3 – 12(2a + 3b)2

= 4 (2a + 3b)2 [2 (2a + 3b) – 3]

= 4 (2a + 3b)2 [4a + 6b – 3]

(v)

9a (x-2y)4 – 12a (x – 2y)3

= 3a (x – 2y)3 [3(x – 2y) – 4]

=3a(x – 2y)3 [3x -6y – 4]

Question 2 :-

Factorise :
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-2
Answer

(i)

a2 – ab – 3a + 3b

= a (a – b) – 3 (a – b)

= (a – b) (a – 3)

(ii)

x2y – xy2 + 5x – 5y

= xy (x – y) + 5 (x – y)

= (x – y) (xy + 5)

(iii)

a2 – ab (1 – b) – b3 = a2 – ab + ab2 – b3

= a(a – b) + b2 (a – b)

= (a – b) (a + b)2

(iv)

xy2 + (x – 1) y – 1 = xy2+ xy – y – 1

= xy (y + 1) – 1 (y + 1)

= (xy – 1)(y + 1)

(v)

(ax + by)2 + (bx – ay)2

= a2x2 + b2y2 + 2abxy + b2x2 + a2y2 – 2abxy

= a2x2 + b2y2 + b2x2 + a2y2

= a2x2 + a2y2 + b2x2 + b2y2

= a2 (x2 + y2) + b2(x2 + y2)

= (x2 + y2)(a2 + b2)

(vi)

ab(x2 + y2) – xy (a2 + b2)

= abx2 + aby2 – a2xy – b2xy

= abx2 – a2xy + aby2 – b2xy

= abx2 – a2xy – b2xy + aby

= ax (bx – ay) – by (bx – ay)

= (bx – ay)(ax – by)

(vii)

m – 1 – (m-1)2 + am – a

= (m – 1) – (m – 1)2 + a (m – 1)

= (m – 1) (1 – (m – 1) + a)

= (m – 1) (1 – m + 1 + a)

= (m – 1) (2 – m + a)

Question 3 :-

Factorise :
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-3
Answer

(i)

a2 – (b – c)2

= (a – (b – c)) (a + b – c)  …[a2 – b2 = (a – b)(a + b)]

= (a – b + c) (a + b – c)

(ii)

25(2x – y)2 – 16(x – 2y)2

= (5 (2x – y))2 – (4 (x – 2y))2

= [5(2x – y) – 4 (x – 2y)][5(2x – y) + 4(x – 2y)]

= [10x – 5y – 4x + 8y][10x – 5y + 4x – 8y]
….[a2 – b2 = (a – b)(a + b)]

= (6x + 3y)(14x – 13y)

= 3(2x + y)(14x – 13y)

(iii)

16(5x + 4)2 -9(3x – 2)2

= (4(5x + y))2 – (3(3x – 2))2

= [4 (5x + 4) – 3 (3x – 2)] [4(5x + 4) +3(3x – 2)]
…..[a2 – b2 = (a – b)(a + b)]

= (20x + 16 – 9x + 6)(20x + 16 + 9x – 6)

= (11x + 22)(29x + 10)

= 11 (x + 2)(29x + 10)

(iv) 

ICSE Class-8 chapter 13Exe-12 B, img 1

[(a2 – b2) = (a – b)(a + b)] 

(v)

25(x – 2y)2 – 4

= (5(x – 2y))2 – 22

= [5 (x – 2y) – 2] [5 (x – 2y) + 2] …[a2 – b2 = (a – b)(a + b)]

= (5x – 10y – 2)(5x – 10y + 2)

Question 4 :-

Factorise :
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-4
Answer

(i)

a2 – 23a + 42  …[42 = 21 × 2 and 21 + 2 = 23]

= a2 – 21a – 2a + 42

= a(a – 21) – 2(a – 21)

= (a – 21)(a – 2)

(ii)

a2 – 23a -108

= a2 – 27a + 4a – 108  …[27 × 4 = 108 and 27 -4 = 23]

= a(a – 27) + 4(a – 27)

= (a – 27)(a + 4)

(iii)

1 – 18x – 63x2

= 1 – 21x + 3x – 63x2

= 1 (1 – 21x) + 3x (1 – 21x)

= (1 – 21 x) (1 + 3x)

(iv)

5x2 – 4xy – 12y2

= 5x2 – 10xy + 6xy – 12y2

= 5x (x – 2y) + 6y (x – 2y)

= (x – 2y)(5x + 6y)

(v)

x(3x + 14) + 8

= 3x2 + 14x + 8

= 3x2 + 12x +2x +8

= 3x(x + 4) + 2(x + 4)

= (x + 4)(3x + 2)

(vi)

5 – 4x(1 + 3x)

= 5 – 4x – 12x2

= 5 – 10x + 6x – 12x2

= 5(1 – 2x)+ 6x (1 – 2x)

= (1 – 2x)(5 + 6x)

(vii)

x2y2 – 3xy – 40

= x2y2 – 8xy + 5xy – 40

= xy (xy – 8) + 5 (xy – 8)

= (xy – 8)(xy + 5)

(viii)

(3x – 2y)2 – 5(3x – 2y) – 24

= (3x – 2y)2 – 8(3x – 2y) + 3(3x – 2y) – 24

= (3x – 2y) (3x – 2y – 8) + 3 (3x – 2y – 8)

= (3x – 2y – 8)(3x – 2y + 3)

(ix)

12(a + b)2 – (a+ b) – 35

= 12 (a + b)2 – 21 (a + b) + 20 (a + b) – 7

= 3(a + b) [4 (a + b) – 7] + 5[4 (a + b) – 7]

= (4a + 4b – 7)(3a + 3b + 5)

Question 5 :-

Factorise :
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-5
Answer

(i)

15(5x – 4)2 – 10(5x – 4)

= 5(5x – 4) [3(5x – 4)2 – 2]

= 5 (5x – 4) [3 (25x2 – 40x + 16) – 2]

= 5(5x – 4) (75x2 – 120x + 46)

(ii)

3a2x – bx + 3a2 – b

= x(3a2 – b) + 1 (3a2 – b)

= (x + 1)(3a2 – b)

(iii)

b(c – d)2 + a(d – c) + 3(c – d)

= b (c – d)2 – a(c – d) + 3(c – d)

= (c – d) [b (c – d) – a + 3]

= (c – d) (bc – bd – a + 3)

(iv)

ax2 + b2y – ab2 – x2y

= ax2 – ab2 + b2y – x2y

= a(x2 – b2) + y(b2 – x2)

= a(x2 – b2) – y(x2 – b2)

= (x2 – b2)(a – y)

= (x – b)(x + b)(a – y)

(v)

1 – 3x – 3y – 4(x + y)2

= 1 – 3(x + y) – 4(x + y)2

= 1 – 4(x + y) + (x + y) – 4(x + y)2

= 1[1 – 4(x + y)] + (x + y)[1 – 4(x + y)]

= [1 – 4x – 4y](1 + x + y)

Question 6 :-

Factorise :
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-6
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-6.1
Answer

(i)

2a3 – 50a

= 2a (a2 – 25) = 2a(a2 – 52)

= 2a (a – 5) (a + 5)

(ii)

54a2b2 – 6

= 6(9a2b2 – 1) = 6[(3ab)2 – (1)2]

= 6 (3ab – 1)(3ab + 1)

(iii)

64a2b – 144b3

= 16b (4a2 – 9b2)

= 16b [(2a)2 – (3b)2]

= 16b (2a + 3b)(2a – 3b)

(iv)

(2x – y)3 – (2x – Y)

= (2x – y)[(2x – y)2 – 1]

= (2x – y)(2x – y – 1) (2x – y + 1)

(v)

x2 – 2xy + y2 – z2

= (x2 – 2xy + y2) – z2

= (x – y)2 – (z)2

= (x – y – z)(x – y + z)

(vi)

x2 – y2 – 2yz – z2

= x2 – (y2 + 2yz + z2)

= x2 – (y + x)2

= (x – y – z)(x + y + z)

(vii)

7a5 – 567a

= 7a(a4 – 81)

= 7a (a2)2 – (9)2

= 7a (a2 + 9) (a2 – 9)

= 7a (a2 + 9) ((a)2 – (3)2)

= 7a (a2 + 9) (a + 3)(a – 3)

(viii)

7a5 – 567a

= 7a(a4 – 81)

= 7a (a2)2 – (9)2

= 7a (a2 + 9) (a2 – 9)

= 7a (a2 + 9) ((a)2 – (3)2)

= 7a (a2 + 9) (a + 3)(a – 3)

Question 7 :-

Factorise xy2 – xz2, Hence, find the value of:
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-7
Answer

(i)

xy2 – xz2 = x(y2 – z2) = x(y – z)(y + z)

9 x 82 – 9 x 22

= 9 (82 – 22)

= 9(8 – 2)(8 + 2)

= 9 (6) (10) = 540

(ii)

xy2 – xz2 = x(y2 – z2) = x(y – z)(y + z)

40 x 5.52 – 40 x 4.52

= 40 (5.5)2 – (4.5)2

= 40 (5.5 – 4.5) (5.5 + 4.5)

= 40 (1) (10) = 400

Question 8 :-

Factorise :
selina-concise-mathematics-class-8-icse-solutions-factorisation-F-8
Answer

(i)

(a – 3b)2 – 36 b2

= (a – 3b)2 – (6b)2

= (a – 3b + 6b) (a – 3b – 6b)

= (a + 3b)(a – 9b)  ….[a2 – b2 = (a + b)(a – b)]

(ii)

25(a – 5b)2 – 4(a – 3b)2

= [5 (a – 5b)]2 – [2(a – 3b)]2

= (5a – 25b)2 – (2a – 6b)

= (5a – 25b + 2a – 6b)(5a – 25b – 2a + 6b)
…..[a2 – b2 = (a + b)(a – b)]

= (7a – 31b)(3a – 19b)

(iii)

a2 – 0·36 b2

=  (a)2 – (0.6b)2

= (a + 0.6b)(a – 0.6b)      …[a2 – b2 = (a + b)(a – b)]

(iv)

a4 – 625

= (a2)2 – (25)2

= (a2 + 25) (a2 – 25)    ….[a2 – b2 = (a + b)(a – b)]

= (a2 + 25) {(a)2 – (5)2}

= (a2 + 25) (a + 5)(a – 5)

(v)

x4 – 5x2 – 36

= (x2)2 – 5x2 – 36

= (x2)2 – 9x2 + 4x2 – 36    …{∵ -36 = -9 × 4 }
{-5 = -9 + 4}

= x2 (x2 – 9) +  (x2 – 9)

= (x2 – 9)(x2 + 4)

= [x2 – (3)2] [x2 + 4]

= (x + 3)(x – 3)(x2 + 4)

= (x2 +4) (x + 3)(x – 3)

(vi)

15(2x – y)2 – 16(2x – y) – 15

= Let 2x – y = a, then

15a2 – 16a – 15

= 15a2 – 25a + 9a – 15
…{15 × (-15) = -225 , -225 = -25 × 9 , -16 = -25 + 9}

= 5a (3a – 5) + 3(3a – 5)

= (3a – 5)(5a + 3)

= [3 (2x – y) – 5][5 (2x – y) + 3]

= (6x – 3y – 5)(10x – 5y + 3)

Question 9 :-

Factorise a2b – b3 Using this result, find the value of 1012 × 100 – 1003.
Answer

a2b – b3

b(a2 – b2)

b(a + b)(a – b)

Now,

1012 × 100 – 1003

= 100 (1012 – 1002)

= 100(101 + 100)(101 – 100)

= 100(201)(1)

= 20100

Question 10 :-

Evaluate (using factors): 3012 × 300 – 3003.
Answer

3012 x 300 – 3003

= 300 (3012 – 3002)

= 300 (301 + 300)(301 – 300)

= 300 (601)(1)

= 180300

 

— End of Factorisation ICSE Class-8th Solutions :–

Return to  Concise Selina Maths Solutions for ICSE Class -8 


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