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RD Sharma solutions for Class 8 Mathematics chapter 7 - Factorization

Mathematics for Class 8 by R D Sharma (2019-2020 Session)

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RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

Mathematics for Class 8 by R D Sharma (2019-2020 Session) - Shaalaa.com

Chapter 7: Factorization

Ex. 7.10Ex. 7.20Ex. 7.30Ex. 7.40Ex. 7.50Ex. 7.60Ex. 7.70Ex. 7.90

Chapter 7: Factorization Exercise 7.10 solutions [Pages 3 - 4]

Ex. 7.10 | Q 1 | Page 3

Find the greatest common factor (GCF/HCF) of the following polynomial:
2x2 and 12x2

Ex. 7.10 | Q 2 | Page 3

Find the greatest common factor (GCF/HCF) of the following polynomial:
6x3y and 18x2y3

Ex. 7.10 | Q 3 | Page 3

Find the greatest common factor (GCF/HCF) of the following polynomial:
7x, 21x2 and 14xy2

Ex. 7.10 | Q 4 | Page 3

Find the greatest common factor (GCF/HCF) of the following polynomial:
42x2yz and 63x3y2z3

Ex. 7.10 | Q 5 | Page 3

Find the greatest common factor (GCF/HCF) of the following polynomial:
12ax2, 6a2x3 and 2a3x5

Ex. 7.10 | Q 6 | Page 3

Find the greatest common factor (GCF/HCF) of the following polynomial:
9x2, 15x2y3, 6xy2 and 21x2y2

Ex. 7.10 | Q 7 | Page 3

Find the greatest common factor (GCF/HCF) of the following polynomial:
4a2b3, −12a3b, 18a4b3

Ex. 7.10 | Q 8 | Page 3

Find the greatest common factor (GCF/HCF) of the following polynomial:
6x2y2, 9xy3, 3x3y2

Ex. 7.10 | Q 9 | Page 4

Find the greatest common factor (GCF/HCF) of the following polynomial:
a2b3, a3b2

Ex. 7.10 | Q 10 | Page 4

Find the greatest common factor (GCF/HCF) of the following polynomial:
36a2b2c4, 54a5c2, 90a4b2c2

Ex. 7.10 | Q 11 | Page 4

Find the greatest common factor (GCF/HCF) of the following polynomial:
x3, − yx2

Ex. 7.10 | Q 12 | Page 4

Find the greatest common factor (GCF/HCF) of the following polynomial:
15a3, − 45a2, − 150a

Ex. 7.10 | Q 13 | Page 4

Find the greatest common factor (GCF/HCF) of the following polynomial:
2x3y2, 10x2y3, 14xy

Ex. 7.10 | Q 14 | Page 4

Find the greatest common factor (GCF/HCF) of the following polynomial:
14x3y5, 10x5y3, 2x2y2

Ex. 7.10 | Q 15 | Page 4

Find the greatest common factor of the terms in each of the following expression:
5a4 + 10a3 − 15a2

Ex. 7.10 | Q 16 | Page 4

Find the greatest common factor of the terms in each of the following expression:
2xyz + 3x2y + 4y2

Ex. 7.10 | Q 17 | Page 4

Find the greatest common factor of the terms in each of the following expression:
3a2b2 + 4b2c2 + 12a2b2c2

Chapter 7: Factorization Exercise 7.20 solutions [Page 5]

Ex. 7.20 | Q 1 | Page 5

Factorize the following:
3x − 9

Ex. 7.20 | Q 2 | Page 5

Factorize the following:
5x − 15x2

Ex. 7.20 | Q 3 | Page 5

Factorize the following:
20a12b2 − 15a8b4

Ex. 7.20 | Q 4 | Page 5

Factorize the following:
72x6y7 − 96x7y6

Ex. 7.20 | Q 5 | Page 5

Factorize the following:
20x3 − 40x2 + 80x

Ex. 7.20 | Q 6 | Page 5

Factorize the following:
2x3y2 − 4x2y3 + 8xy4

Ex. 7.20 | Q 7 | Page 5

Factorize the following:
10m3n2 + 15m4n − 20m2n3

Ex. 7.20 | Q 8 | Page 5

Factorize the following:
2a4b4 − 3a3b5 + 4a2b5

Ex. 7.20 | Q 9 | Page 5

Factorize the following:
28a2 + 14a2b2 − 21a4

Ex. 7.20 | Q 10 | Page 5

Factorize the following:
a4b − 3a2b2 − 6ab3

Ex. 7.20 | Q 11 | Page 5

Factorize the following:
2l2mn - 3lm2n + 4lmn2

Ex. 7.20 | Q 12 | Page 5

Factorize the following:
x4y2 − x2y4 − x4y4

Ex. 7.20 | Q 13 | Page 5

Factorize the following:
9x2y + 3axy

Ex. 7.20 | Q 14 | Page 5

Factorize the following:
16m − 4m2

Ex. 7.20 | Q 15 | Page 5

Factorize the following:
−4a2 + 4ab − 4ca

Ex. 7.20 | Q 16 | Page 5

Factorize the following:
x2yz + xy2z + xyz2

Ex. 7.20 | Q 17 | Page 5

Factorize the following:
ax2y + bxy2 + cxyz

Chapter 7: Factorization Exercise 7.30 solutions [Page 7]

Ex. 7.30 | Q 1 | Page 7

Factorize each of the following algebraic expressions:
6x(2x − y) + 7y(2x − y)

Ex. 7.30 | Q 2 | Page 7

Factorize each of the following algebraic expressions:
2r(y − x) + s(x − y)

Ex. 7.30 | Q 3 | Page 7

Factorize each of the following algebraic expressions:
7a(2x − 3) + 3b(2x − 3)

Ex. 7.30 | Q 4 | Page 7

Factorize each of the following algebraic expressions:
9a(6a − 5b) −12a2(6a − 5b)

Ex. 7.30 | Q 5 | Page 7

Factorize each of the following algebraic expressions:
5(x − 2y)2 + 3(x − 2y)

Ex. 7.30 | Q 6 | Page 7

Factorize each of the following algebraic expressions:
16(2l − 3m)2 −12(3m − 2l)

Ex. 7.30 | Q 7 | Page 7

Factorize each of the following algebraic expressions:
3a(x − 2y) −b(x − 2y)

Ex. 7.30 | Q 8 | Page 7

Factorize each of the following algebraic expressions:
a2(x + y) +b2(x + y) +c2(x + y)

Ex. 7.30 | Q 9 | Page 7

Factorize each of the following algebraic expressions:
(x − y)2 + (x − y)

Ex. 7.30 | Q 10 | Page 7

Factorize each of the following algebraic expressions:
6(a + 2b) −4(a + 2b)2

Ex. 7.30 | Q 11 | Page 7

Factorize each of the following algebraic expressions:
a(x − y) + 2b(y − x) + c(x − y)2

Ex. 7.30 | Q 12 | Page 7

Factorize each of the following algebraic expressions:
−4(x − 2y)2 + 8(x −2y)

Ex. 7.30 | Q 13 | Page 7

Factorize each of the following algebraic expressions:
x3(a − 2b) + x2(a − 2b)

Ex. 7.30 | Q 14 | Page 7

Factorize each of the following algebraic expressions:
(2x − 3y)(a + b) + (3x − 2y)(a + b)

Ex. 7.30 | Q 15 | Page 7

Factorize each of the following algebraic expressions:
4(x + y) (3a − b) +6(x + y) (2b − 3a)

Chapter 7: Factorization Exercise 7.40 solutions [Page 12]

Ex. 7.40 | Q 1 | Page 12

Factorize each of the following expressions:
qr − pr + qs − ps

Ex. 7.40 | Q 2 | Page 12

Factorize each of the following expressions:
p2q − pr2 − pq + r2

Ex. 7.40 | Q 3 | Page 12

Factorize each of the following expressions:
1 + x + xy + x2y

Ex. 7.40 | Q 4 | Page 12

Factorize each of the following expressions:
ax + ay − bx − by

Ex. 7.40 | Q 5 | Page 12

Factorize each of the following expressions:
xa2 + xb2 − ya2 − yb2

Ex. 7.40 | Q 6 | Page 12

Factorize each of the following expressions:
x2 + xy + xz + yz

Ex. 7.40 | Q 7 | Page 12

Factorize each of the following expressions:
2ax + bx + 2ay + by

Ex. 7.40 | Q 8 | Page 12

Factorize each of the following expressions:
ab − by − ay + y2

Ex. 7.40 | Q 9 | Page 12

Factorize each of the following expressions:
axy + bcxy − az − bcz

Ex. 7.40 | Q 10 | Page 12

Factorize each of the following expressions:
lm2 − mn2 − lm + n2

Ex. 7.40 | Q 11 | Page 12

Factorize each of the following expressions:
x3 − y2 + x − x2y2

Ex. 7.40 | Q 12 | Page 12

Factorize each of the following expressions:
6xy + 6 − 9y − 4x

Ex. 7.40 | Q 13 | Page 12

Factorize each of the following expressions:
x2 − 2ax − 2ab + bx

Ex. 7.40 | Q 14 | Page 12

Factorize each of the following expressions:
x3 − 2x2y + 3xy2 − 6y3

Ex. 7.40 | Q 15 | Page 12

Factorize each of the following expression:
abx2 + (ay − b) x − y

Ex. 7.40 | Q 16 | Page 12

Factorize each of the following expression:
(ax + by)2 + (bx − ay)2

Ex. 7.40 | Q 17 | Page 12

Factorize each of the following expression:
16(a − b)3 − 24 (a − b)2

Ex. 7.40 | Q 18 | Page 12

Factorize each of the following expression:
ab(x2 + 1) + x(a2 + b2)

Ex. 7.40 | Q 19 | Page 12

Factorize each of the following expression:
a2x2 + (ax2 + 1)x + a

Ex. 7.40 | Q 20 | Page 12

Factorize each of the following expression:
a(a − 2b − c) + 2bc

Ex. 7.40 | Q 21 | Page 12

Factorize each of the following expression:
a(a + b − c) − bc

Ex. 7.40 | Q 22 | Page 12

Factorize each of the following expression:
x2 − 11xy − x + 11y

Ex. 7.40 | Q 23 | Page 12

Factorize each of the following expression:
ab − a − b + 1

Ex. 7.40 | Q 24 | Page 12

Factorize each of the following expression:
x2 + y − xy − x

Chapter 7: Factorization Exercise 7.50 solutions [Page 17]

Ex. 7.50 | Q 1 | Page 17

Factorize each of the following expression:
16x2 − 25y2

Ex. 7.50 | Q 2 | Page 17

Factorize each of the following expression:
27x2 − 12y2

Ex. 7.50 | Q 3 | Page 17

Factorize each of the following expression:
144a2 − 289b2

Ex. 7.50 | Q 4 | Page 17

Factorize each of the following expression:
12m2 − 27

Ex. 7.50 | Q 5 | Page 17

Factorize each of the following expression:
125x2 − 45y2

Ex. 7.50 | Q 6 | Page 17

Factorize each of the following expression:
144a2 − 169b2

Ex. 7.50 | Q 7 | Page 17

Factorize each of the following expression:
(2a − b)2 − 16c2

Ex. 7.50 | Q 8 | Page 17

Factorize each of the following expression:
(x + 2y)2 − 4(2x − y)2

Ex. 7.50 | Q 9 | Page 17

Factorize each of the following expression:
3a5 − 48a3

Ex. 7.50 | Q 10 | Page 17

Factorize each of the following expression:
a4 − 16b4

Ex. 7.50 | Q 11 | Page 17

Factorize each of the following expression:
x8 − 1

Ex. 7.50 | Q 12 | Page 17

Factorize each of the following expression:
64 − (a + 1)2

Ex. 7.50 | Q 13 | Page 17

Factorize each of the following expression:
36l2 − (m + n)2

Ex. 7.50 | Q 14 | Page 17

Factorize each of the following expression:
25x4y4 − 1

Ex. 7.50 | Q 15 | Page 17

Factorize each of the following expression:

\[a^4 - \frac{1}{b^4}\]
Ex. 7.50 | Q 16 | Page 17

Factorize each of the following expression:
x3 − 144x

Ex. 7.50 | Q 17 | Page 17

Factorize each of the following expression:
(x - 4y)2 − 625

Ex. 7.50 | Q 18 | Page 17

Factorize each of the following expression:
9(a − b)2 − 100(x − y)2

Ex. 7.50 | Q 19 | Page 17

Factorize each of the following expression:
(3 + 2a)2 − 25a2

Ex. 7.50 | Q 20 | Page 17

Factorize each of the following expression:
(x + y)2 − (a − b)2

Ex. 7.50 | Q 21 | Page 17

Factorize each of the following expression:
\[\frac{1}{16} x^2 y^2 - \frac{4}{49} y^2 z^2\]

Ex. 7.50 | Q 22 | Page 17

Factorize each of the following expression:
75a3b2 - 108ab4

Ex. 7.50 | Q 23 | Page 17

Factorize each of the following expression:
x5 − 16x3

Ex. 7.50 | Q 24 | Page 17

Factorize each of the following expression:

\[\frac{50}{x^2} - \frac{2 x^2}{81}\]
Ex. 7.50 | Q 25 | Page 17

Factorize each of the following expression:
256x5 − 81x

Ex. 7.50 | Q 26 | Page 17

Factorize each of the following expression:
a4 − (2b + c)4

Ex. 7.50 | Q 27 | Page 17

Factorize each of the following expression:
(3x + 4y)4 − x4

Ex. 7.50 | Q 28 | Page 17

Factorize each of the following expression:
p2q2 − p4q4

Ex. 7.50 | Q 29 | Page 17

Factorize each of the following expression:
3x3y − 243xy3

Ex. 7.50 | Q 30 | Page 17

Factorize each of the following expression:
a4b4 − 16c4

Ex. 7.50 | Q 31 | Page 17

Factorize each of the following expression:
x4 − 625

Ex. 7.50 | Q 32 | Page 17

Factorize each of the following expression:
x4 − 1

Ex. 7.50 | Q 33 | Page 17

Factorize each of the following expression:
49(a − b)2 − 25(a + b)2

Ex. 7.50 | Q 34 | Page 17

Factorize each of the following expression:
x − y − x2 + y2

Ex. 7.50 | Q 35 | Page 17

Factorize each of the following expression:
16(2x − 1)2 − 25y2

Ex. 7.50 | Q 36 | Page 17

Factorize each of the following expression:
4(xy + 1)2 − 9(x − 1)2

Ex. 7.50 | Q 37 | Page 17

Factorize each of the following expression:
(2x + 1)2 − 9x4

Ex. 7.50 | Q 38 | Page 17

Factorize each of the following expression:
x4 − (2y − 3z)2

Ex. 7.50 | Q 39 | Page 17

Factorize each of the following expression:
a2 − b2 + a − b

Ex. 7.50 | Q 40 | Page 17

Factorize each of the following expression:
16a4 − b4

Ex. 7.50 | Q 41 | Page 17

Factorize each of the following expression:
a4 − 16(b − c)4

Ex. 7.50 | Q 42 | Page 17

Factorize each of the following expression:
2a5 − 32a

Ex. 7.50 | Q 43 | Page 17

Factorize each of the following expression:
a4b4 − 81c4

Ex. 7.50 | Q 44 | Page 17

Factorize each of the following expression:
xy9 − yx9

Ex. 7.50 | Q 45 | Page 17

Factorize each of the following expression:
x3 − x

Ex. 7.50 | Q 46 | Page 17

Factorize each of the following expression:
18a2x2 − 32

Chapter 7: Factorization Exercise 7.60 solutions [Pages 22 - 23]

Ex. 7.60 | Q 1 | Page 22

Factorize each of the following algebraic expression:
4x2 + 12xy +9y2

Ex. 7.60 | Q 2 | Page 22

Factorize each of the following algebraic expression:
9a2 − 24ab + 16b2

Ex. 7.60 | Q 3 | Page 22

Factorize each of the following algebraic expression:
p2q2 − 6pqr + 9r2

Ex. 7.60 | Q 4 | Page 22

Factorize each of the following algebraic expression:
36a2 + 36a + 9

Ex. 7.60 | Q 5 | Page 23

Factorize each of the following algebraic expression:
a2 + 2ab + b2 − 16

Ex. 7.60 | Q 6 | Page 23

Factorize each of the following algebraic expression:
9z2 − x2 + 4xy − 4y2

Ex. 7.60 | Q 7 | Page 23

Factorize each of the following algebraic expression:
9a4 − 24a2b2 + 16b4 − 256

Ex. 7.60 | Q 8 | Page 23

Factorize each of the following algebraic expression:
16 − a6 + 4a3b3 − 4b6

Ex. 7.60 | Q 9 | Page 23

Factorize each of the following algebraic expression:
a2 − 2ab + b2 − c2

Ex. 7.60 | Q 10 | Page 23

Factorize each of the following algebraic expression:
x2 + 2x + 1 − 9y2

Ex. 7.60 | Q 11 | Page 23

Factorize each of the following algebraic expression:
a2 + 4ab + 3b2

Ex. 7.60 | Q 12 | Page 23

Factorize each of the following algebraic expression:
96 − 4x − x2

Ex. 7.60 | Q 13 | Page 23

Factorize each of the following algebraic expression:
a4 + 3a2 +4

Ex. 7.60 | Q 14 | Page 23

Factorize each of the following algebraic expression:
4x4 + 1

Ex. 7.60 | Q 15 | Page 23

Factorize each of the following algebraic expression:
4x4 + y4

Ex. 7.60 | Q 16 | Page 23

Factorize each of the following algebraic expression:
(x + 2)2 − 6(x + 2) + 9

Ex. 7.60 | Q 17 | Page 23

Factorize each of the following algebraic expression:
25 − p2 − q2 − 2pq

Ex. 7.60 | Q 18 | Page 23

Factorize each of the following algebraic expression:
x2 + 9y2 − 6xy − 25a2

Ex. 7.60 | Q 19 | Page 23

Factorize each of the following algebraic expression:
49 − a2 + 8ab − 16b2

Ex. 7.60 | Q 20 | Page 23

Factorize each of the following algebraic expression:
a2 − 8ab + 16b2 − 25c2

Ex. 7.60 | Q 21 | Page 23

Factorize each of the following algebraic expression:
x2 − y2 + 6y − 9

Ex. 7.60 | Q 22 | Page 23

Factorize each of the following algebraic expression:
25x2 − 10x + 1 − 36y2

Ex. 7.60 | Q 23 | Page 23

Factorize each of the following algebraic expression:
a2 − b2 + 2bc − c2

Ex. 7.60 | Q 24 | Page 23

Factorize each of the following algebraic expression:
a2 + 2ab + b2 − c2

Ex. 7.60 | Q 25 | Page 23

Factorize each of the following algebraic expression:
49 − x2 − y2 + 2xy

Ex. 7.60 | Q 26 | Page 23

Factorize each of the following algebraic expression:
a2 + 4b2 − 4ab − 4c2

Ex. 7.60 | Q 27 | Page 23

Factorize each of the following algebraic expression:
x2 − y2 − 4xz + 4z2

Chapter 7: Factorization Exercise 7.70 solutions [Page 27]

Ex. 7.70 | Q 1 | Page 27

Factorize each of the following algebraic expression:
x2 + 12x − 45

Ex. 7.70 | Q 2 | Page 27

Factorize each of the following algebraic expression:
40 + 3x − x2

Ex. 7.70 | Q 3 | Page 27

Factorize each of the following algebraic expression:
a2 + 3a − 88

Ex. 7.70 | Q 4 | Page 27

Factorize each of the following algebraic expression:
a2 − 14a − 51

Ex. 7.70 | Q 5 | Page 27

Factorize each of the following algebraic expression:
x2 + 14x + 45

Ex. 7.70 | Q 6 | Page 27

Factorize each of the following algebraic expression:
x2 − 22x + 120

Ex. 7.70 | Q 7 | Page 27

Factorize each of the following algebraic expression:
x2 − 11x − 42

Ex. 7.70 | Q 8 | Page 27

Factorize each of the following algebraic expression:
a2 + 2a − 3

Ex. 7.70 | Q 9 | Page 27

Factorize each of the following algebraic expression:
a2 + 14a + 48

Ex. 7.70 | Q 10 | Page 27

Factorize each of the following algebraic expression:
x2 − 4x − 21

Ex. 7.70 | Q 11 | Page 27

Factorize each of the following algebraic expression:
y2 + 5y − 36

Ex. 7.70 | Q 12 | Page 27

Factorize each of the following algebraic expression:
(a2 − 5a)2 − 36

Ex. 7.70 | Q 13 | Page 27

Factorize each of the following algebraic expression:
(a + 7)(a − 10) + 16

Chapter 7: Factorization Exercise 7.90 solutions [Pages 32 - 33]

Ex. 7.90 | Q 1 | Page 32

Factorize each of the following quadratic polynomials by using the method of  completing the square:
p2 + 6p + 8

Ex. 7.90 | Q 2 | Page 32

Factorize each of the following quadratic polynomials by using the method of completing the square:
q2 − 10q + 21

Ex. 7.90 | Q 3 | Page 32

Factorize each of the following quadratic polynomials by using the method of completing the square:
4y2 + 12y + 5

Ex. 7.90 | Q 4 | Page 32

Factorize each of the following quadratic polynomials by using the method of completing the square:
p2 + 6p − 16

Ex. 7.90 | Q 5 | Page 32

Factorize each of the following quadratic polynomials by using the method of completing the square:
x2 + 12x + 20

Ex. 7.90 | Q 6 | Page 32

Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 − 14a − 51

Ex. 7.90 | Q 7 | Page 33

Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 + 2a − 3

Ex. 7.90 | Q 8 | Page 33

Factorize each of the following quadratic polynomials by using the method of completing the square:
4x2 − 12x + 5

Ex. 7.90 | Q 9 | Page 33

Factorize each of the following quadratic polynomials by using the method of completing the square:
y2 − 7y + 12

Ex. 7.90 | Q 10 | Page 33

Factorize each of the following quadratic polynomials by using the method of completing the square:
z2 − 4z − 12

Chapter 7: Factorization

Ex. 7.10Ex. 7.20Ex. 7.30Ex. 7.40Ex. 7.50Ex. 7.60Ex. 7.70Ex. 7.90

RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

Mathematics for Class 8 by R D Sharma (2019-2020 Session) - Shaalaa.com

RD Sharma solutions for Class 8 Mathematics chapter 7 - Factorization

RD Sharma solutions for Class 8 Maths chapter 7 (Factorization) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Mathematics chapter 7 Factorization are Factors of Natural Numbers, Factors of Algebraic Expressions, Method of Common Factors, Factorisation by Regrouping Terms, Factorisation Using Identities, Factors of the Form ( x + a) ( x + b), Division of Algebraic Expressions - Division of a Monomial by Another Monomial, Division of Algebraic Expressions - Division of a Polynomial by a Monomial, Division of Algebraic Expressions Continued (Polynomial รท Polynomial), Concept of Find the Error, Method of Completing the Square.

Using RD Sharma Class 8 solutions Factorization exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer RD Sharma Textbook Solutions to score more in exam.

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