Frank ICSE Class 8 Solutions Chapter 11

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Frank ICSE Mathematics Class 8 Solutions Chapter 11 Factorisation

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Frank ICSE Mathematics Class 8 Math Book, Chapter 11, Factorisation. Here students can easily find step by step solutions of all the problems for Factorisation, Exercise 11.1, 11.2 and 11.3 Also our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 11 solutions. Here in this post all the solutions are based on latest Syllabus.

Factorisation Exercise 11.1 Solution :

Question no – (1)

Solution :

The common factor will be

= 4abc

Question number – (2)

Solution :

The common factor in the expression will be

= 2xy

Question no – (3)

Solution :

= 18m²n – 24mn² + 30m²n²

= 6mn (3m – 4n + 5mn)

Question no – (4)

Solution :

(a) 24xy = 2 × 2 × 2 × 3 × x × y

= 8yz = 2 × 2 × 2 × y × 2

Common factor 2 × 2 × 2 × y = 8y

(b) 15a²b = 3 × 5 × a × a × b

= 12ab² = 2 × 2 × 3 × a × b × b

Common factor = 3 × a × b = 3ab

(c) 21p⁴q² = 3 × 7 × p × p × p × q × q

= – 14p²q² = (- 2) × 7 × p × q × q × q × q

= – 35p³q³ = (- 5) × 7 × p × p × p × q × q × q

(d) 25ab = 5 × 5 × b × c

= 50bc = 2 × 5 × 5 × b × c

Common factor = 5 × b = 56

(e) 15 (xy + 4) = 3 × 5 × (xy + 4)

= 12(xy + 4)² = 2 × 2 × 3 × (xy + 4) × (xy + 4)

Common factor = 3 × (xy + 4)

= 3(xy + 4)

Question no – (5)

Solution :

(a) 9x – 72

= 9 (x – 8)

(b) 16a¹³b⁷ – 24a⁷b¹¹

= 8a⁷b⁷(a⁶ – b⁴)

= 8⁷b⁷ (a³ + b²) (a³ – b²)

(c) 2x³y² + 10x² – 14xy

= 2xy (x²y + 5xy² – 14)

(d) 18x²yz + 36xy²z + 27xyz²

= 9xyz² (2x + 4y + 3z)

(e) 36a²b²c² – 54a³b³c³ + 71a⁴b⁴c⁴

= 18a²b²c² (2 – 3abc + 4a²b²c²)

(f) 15m²n – 45mn² + 75mn

= 15mn (m – 3x + 5)

Question no – (6)

Solution :

(a) a² + ab + 9a + 9b

= a(a + b) + 9 (a + 9)

= (a + b) (a + 9)

(b) 24mn – 21n + 8m – 7

= 3n (8m – 7) + 1 (8m – 7)

= (8m – 7) (3n + 1)

(c) x³ – 2x² + 3xy² – 6y³

= x² (x – 2y) + 3y² (x – 2y)

= (x – 2y) (x² + 3y²)

(d) 18x²y² + 4xy² + 9x³y³ + 8y

= 18x²y² + 9x³y³ + 4xy² +8y

= 9x²y² (2 + xy) + 4y (xy+ 2)

= (xy + 2) (9x²y² + 4y)

(e) (2a – 3b) 9m + n) + (3a – 2b) (m + n)

= (m + n) [(2a – 3b) + (3a – 2b)

= (m +n) [(2a + 3a) + (- 3a – 2b)

= (m+ n) [5a – 5b] = 5 (m + n) (a – b)

(f) 4 (x – y)² + 12 (x – y)

= 4 (x – y) [(x – y) + 3]

= 4 (x – y) (x – y + 3)

Question no – (7)

Solution :

(a) (9x² +24x + 16)

= (3x)² + 2.3x. 4 + (4)²

= (3x + 4)²

(b) (4x²y² – 4xyz + z²)

= (2xy)² – 2.2xyz + (z)²

= (2xy – z)

(c) x² + 2 + 1/x²

= (x)² + 2.x + (1/x)

= (x + 1/x)²

(d) x⁴ – 10x²y² + 25y⁴

= (x2)² – 2.5x² + (5y²)²

= (x² – 5y²)²

Question no – (8)

Solution :

(a) 64a² – 25b²

= (8a)² – (5b)²

= (8a + 5b) (8a + 5b)

(b) 121a² – 144b²

= (11a)² – (12b)²

= (11a + 12b) (11a – 12b)

(c) 81a² – 49b²

= (90)² – (7b)²

= (9a + 7b) (9a – 7b)

(d) (3x + 7)² – y²

= (3x + 7 + y) (3x + 7 – y)

(e) (x + 2y)² – 4 (2x – y)²

= (x + 2y)²

= (x + 2y)² – [2(2x –y)]²

= {(x + 2y) + 2(2x – y)} {(x + 2y) – 2 (2x – y)

(f) 36 (a + 2b)² – 49 (2a – b)²

= {6(a + 2b)}² – {7 (2a – b)}²

= {6(a + 2b) + 7 (2a – b)} {6 (a + 2b) – 7 (2a – b)}

(g) 25 (2a + b)² – 4 ( – b)²

= {3(2a + b)}² – {2(a – b)}²

= {5(x + y) + 4 (x – y)} {5 (x + y) – 4 (x – y)}

Question no – (9)

Solution :

(a) x⁴ – 16 = (x² + 4) (x² – 4)

= (x² + 4) (x + 2) (x – 2)

(b) 256x⁴ – y⁴ = (16x² + y²) (16x² – y²)

= (16x² + y²) (4x + y) (4x – y)

(c) 81x⁴ – 625

= (9x² + 25) (9x² – 25)

= (9x² + 25) (3x + 5) (3x – 5)

(d) 2x²  – 50y²

= (x² – 25y²)

= 2 (x + 5y) (x – 5y)

(e) 3x² – 108y²

= (3 (x² – 36y²)

= 3 (x + 6y) (x – 6y)

(f) 5a² – 80b²

= 5 (a² – 16b²)

= 5(a + 4b) (a – 4b)

(g) 4x² – 100y²

= 4(x² – 25y²) =

= 4 (x + 5y) (x – 5y)

(h) 16x⁴ – 625y⁴

= (4x² + 25y²) (4x² – 25y²)

= (4x² – 25y²) (2x + 5y) (2x – 5y)

Question no – (10)

Solution :

(a) 78 × 82

= (80 – 2) (80 + 2)

= (80)² – (2)²

= 6400 – 4

= 6396

(b) 103 × 97

= (100 + 3) (100 – 3)

= (100)² – (3)²

= 10000 – 9

= 9991

(c) 9.2 × 8.8 = (9 + 0.2)

= (9)² – (0.2)²

= 81 – 0.4

= 80.06

(d) 159 × 161 = (160 – 1) (160 + 1)

= (160)² – (1)²

= 25600 – 1

= 25599

(e) 97² – 96²

= (97 + 96) (97 – 96)

= 193 × 1

= 193

(f) 225² – 224²

= (225 + 224) (225 – 224)

= 449 × 1

= 449

(g) 63² – 61²

= (63 + 61) (63 -61)

= 124 × 2

= 248

(h) 203² – 201²

= (203 + 201) (203 – 201)

= 404 × 2

= 808

Factorisation Exercise 11.2 Solution :

Question no – (1)

Solution :

= x² + 11x + 24

= x² + 8x + 3x + 2y

= x (x + 8) + 3 (x + 8)

= (x + 8) (x + 3)

Question no – (2)

Solution :

= a² + 5a – 36

= a² + 9a – 4a – 36

= (a + 9) (a – 4)

Question no – (3)

Solution :

= z² + 14x + 48

= x² + 8x + 6x + 48

= (x + 8) (x + 6)

Question no – (4)

Solution :

= x² + 4x – 231

= x² – 7x + 3x – 21

= (x – 7) (x + 3)

Question no – (5)

Solution :

= x² + 2x – 24

= x² + 6x – 4x – 24

= (x + 6) (x – 4)

Question no – (6)

Solution :

= x² + 2x – 24

= x² + 6x – 4x – 24

= (x + 6) (x – 4)

Question no – (7)

Solution :

= a² – 8 + 15

= a² – 5a – 3a + 15

= (a – 5) (a – 3)

Question no – (8)

Solution :

= x² + 8x – 48

= x² + 12x – 4x – 48 – 48

= (x + 12) (x – 4)

Question no – (9)

Solution :

= 6a² – 13ab + 2b²

= 6a² – 12ab – ab + 2b²

= (a – 2b) (6a – b)

Question no – (10)

Solution :

= 3x² + 22x + 35

= 3x² + 15x + 7x + 35

= (x + 5) (3x + 7)

Question no – (11)

Solution :

= 11m² – 54mn + 63n²

= 11m² – 33mn – 21mn + 63x²

= (m – 3n) (11m – 21x)

Question no – (12)

Solution :

= 2x² + 19xy + 24y²

= 2x² + 16xy + 3xy + 24y²

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

Question no – (13)

Solution :

= x²+ 3xy – 18y²

= x² + 6xy – 3xy – 18y²

= (x + 6y) (x – 3y)

Question no – (14)

Solution :

= 6x² – 7x – 20

= 6x² – 15x + 8x – 20

= (2x – 5) (3x + 4)

Question no – (15)

Solution :

= 2a² – 7a + 6

= 2a² – 4a – 3a + 6

= (a – 2) (2a – 1)

Question no – (16)

Solution :

= 3a² – 10a – 8

= 3a² – 12a + 2a – 8

= (a – 4) (3a + 2)

Question no – (17)

Solution :

= 2x² – 7x + 3

= 2x² – 6x – x + 3

= (x – 3) (2x – 1)

Question no – (18)

Solution :

= 2x² – 5x – 3

= 2x² – 6x + x – 3

= (x – 3) (2x + 1)

Revision Exercise Questions Solution :

Question no – (1)

Solution :

= 9(x + 2)² – 4(x – 1)²

= {3(x + 2)}² – {2(x – 1)}²

= {3(x + 2) + 2(x – 1)} {3 (x + 2) – 2 (x – 1)}

Question no – (2)

Solution :

= (79)² – (21)²

= (79 + 21) (79 – 21)

= 100 × 58

Question no – (3) 

Solution : 

(a) (3×2 + 4x – 20) by (x – 2) 

(b) 12×2 + 25x + 12 by (3x + 4) 

(c) 6×2 + 8x + 2 by (3x + 1) 

(d) 12×2 + 13x – 35 by (3x + 7) 

(e) 3×3 + 2×2 – 19x + 6 by (x – 2)

Question no – (4) 

Solution : 

(a) 5x² – 18x – 8

= 5x² – 20x + 2x – 8

= (x – 4) (5x + 2)

(b) 3x² – 5x – 12

= 3x² – 9x + 4x – 12

= 3x² – 9x + 4x – 12

= (x – 3) (3x + 4)

(c) 6x² – x – 12

= 6x² – 9x + 8x – 12

= (2x – 3) (3x + 4)

(d) 4x² – x – 18

= 4x² – 9x + 8x – 18

= (4x – 9) (x + 2)

(e) 9 (a + 2b)² – 4 (3a – b)}² – {2(3a – b)}²

= {3(a + 2b) + 2(a – b)} {3(a + 2b) – 2 (3a – b)

Next Chapter Solution : 

👉 Chapter 12 👈