#### Chapters

Chapter 2: Powers

Chapter 3: Squares and Square Roots

Chapter 4: Cubes and Cube Roots

Chapter 5: Playing with Numbers

Chapter 6: Algebraic Expressions and Identities

Chapter 7: Factorization

Chapter 8: Division of Algebraic Expressions

Chapter 9: Linear Equation in One Variable

Chapter 10: Direct and Inverse Variations

Chapter 11: Time and Work

Chapter 12: Percentage

Chapter 13: Proft, Loss, Discount and Value Added Tax (VAT)

Chapter 14: Compound Interest

Chapter 15: Understanding Shapes-I (Polygons)

Chapter 16: Understanding Shapes-II (Quadrilaterals)

Chapter 17: Understanding Shapes-III (Special Types of Quadrilaterals)

Chapter 18: Practical Geometry (Constructions)

Chapter 19: Visualising Shapes

Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)

Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Chapter 23: Data Handling-I (Classification and Tabulation of Data)

Chapter 24: Data Handling-II (Graphical Representation of Data as Histograms)

Chapter 25: Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

Chapter 26: Data Handling-IV (Probability)

Chapter 27: Introduction to Graphs

## Chapter 7: Factorization

#### RD Sharma solutions for Class 8 Maths Chapter 7 Factorization Exercise 7.1 [Pages 3 - 4]

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

2x^{2} and 12x^{2}

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

6x^{3}y and 18x^{2}y^{3}

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

7x, 21x^{2} and 14xy^{2}

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

42x^{2}yz and 63x^{3}y^{2}z^{3}

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

12ax^{2}, 6a^{2}x^{3} and 2a^{3}x^{5}

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

9x^{2}, 15x^{2}y^{3}, 6xy^{2} and 21x^{2}y^{2}

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

4a^{2}b^{3}, −12a^{3}b, 18a^{4}b^{3}

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

6x^{2}y^{2}, 9xy^{3}, 3x^{3}y^{2}

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

a^{2}b^{3}, a^{3}b^{2}

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

36a^{2}b^{2}c^{4}, 54a^{5}c^{2}, 90a^{4}b^{2}c^{2}

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

x^{3}, − yx^{2}

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

15a^{3}, − 45a^{2}, − 150a

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

2x^{3}y^{2}, 10x^{2}y^{3}, 14xy

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

14x^{3}y^{5}, 10x^{5}y^{3}, 2x^{2}y^{2}

Find the greatest common factor of the terms in each of the following expression:

5a^{4}^{ }+ 10a^{3} − 15a^{2}

Find the greatest common factor of the terms in each of the following expression:

2xyz + 3x^{2}y + 4y^{2}

Find the greatest common factor of the terms in each of the following expression:

3a^{2}b^{2} + 4b^{2}c^{2} + 12a^{2}b^{2}c^{2}

#### RD Sharma solutions for Class 8 Maths Chapter 7 Factorization Exercise 7.2 [Page 5]

Factorize the following:

3x − 9

Factorize the following:

5x − 15x^{2}

Factorize the following:

20a^{12}b^{2} − 15a^{8}b^{4}

Factorize the following:

72x^{6}y^{7} − 96x^{7}y^{6}

Factorize the following:

20x^{3} − 40x^{2} + 80x

Factorize the following:

2x^{3}y^{2} − 4x^{2}y^{3} + 8xy^{4}

Factorize the following:

10m^{3}n^{2} + 15m^{4}n − 20m^{2}n^{3}

Factorize the following:

2a^{4}b^{4} − 3a^{3}b^{5} + 4a^{2}b^{5}

Factorize the following:

28a^{2} + 14a^{2}b^{2} − 21a^{4}

Factorize the following:

a^{4}b − 3a^{2}b^{2} − 6ab^{3}

Factorize the following:

2l^{2}mn - 3lm^{2}n + 4lmn^{2}

Factorize the following:

x^{4}y^{2} − x^{2}y^{4} − x^{4}y^{4}

Factorize the following:

9x^{2}y + 3axy

Factorize the following:

16m − 4m^{2}

Factorize the following:

−4a^{2} + 4ab − 4ca

Factorize the following:

x^{2}yz + xy^{2}z + xyz^{2}

Factorize the following:

ax^{2}y + bxy^{2} + cxyz

#### RD Sharma solutions for Class 8 Maths Chapter 7 Factorization Exercise 7.3 [Page 7]

Factorize each of the following algebraic expressions:

6x(2x − y) + 7y(2x − y)

Factorize each of the following algebraic expressions:

2r(y − x) + s(x − y)

Factorize each of the following algebraic expressions:

7a(2x − 3) + 3b(2x − 3)

Factorize each of the following algebraic expressions:

9a(6a − 5b) −12a^{2}(6a − 5b)

Factorize each of the following algebraic expressions:

5(x − 2y)^{2} + 3(x − 2y)

Factorize each of the following algebraic expressions:

16(2l − 3m)^{2} −12(3m − 2l)

Factorize each of the following algebraic expressions:

3a(x − 2y) −b(x − 2y)

Factorize each of the following algebraic expressions:

a^{2}(x + y) +b^{2}(x + y) +c^{2}(x + y)

Factorize each of the following algebraic expressions:

(x − y)^{2} + (x − y)

Factorize each of the following algebraic expressions:

6(a + 2b) −4(a + 2b)^{2}

Factorize each of the following algebraic expressions:

a(x − y) + 2b(y − x) + c(x − y)^{2}

Factorize each of the following algebraic expressions:

−4(x − 2y)^{2} + 8(x −2y)

Factorize each of the following algebraic expressions:

x^{3}(a − 2b) + x^{2}(a − 2b)

Factorize each of the following algebraic expressions:

(2x − 3y)(a + b) + (3x − 2y)(a + b)

Factorize each of the following algebraic expressions:

4(x + y) (3a − b) +6(x + y) (2b − 3a)

#### RD Sharma solutions for Class 8 Maths Chapter 7 Factorization Exercise 7.4 [Page 12]

Factorize each of the following expressions:

qr − pr + qs − ps

Factorize each of the following expressions:

p^{2}q − pr^{2} − pq + r^{2}

Factorize each of the following expressions:

1 + x + xy + x^{2}y

Factorize each of the following expressions:

ax + ay − bx − by

Factorize each of the following expressions:

xa^{2} + xb^{2} − ya^{2} − yb^{2}

Factorize each of the following expressions:

x^{2} + xy + xz + yz

Factorize each of the following expressions:

2ax + bx + 2ay + by

Factorize each of the following expressions:

ab − by − ay + y^{2}

Factorize each of the following expressions:

axy + bcxy − az − bcz

Factorize each of the following expressions:

lm^{2} − mn^{2} − lm + n^{2}

Factorize each of the following expressions:

x^{3} − y^{2} + x − x^{2}y^{2}

Factorize each of the following expressions:

6xy + 6 − 9y − 4x

Factorize each of the following expressions:

x^{2} − 2ax − 2ab + bx

Factorize each of the following expressions:

x^{3} − 2x^{2}y + 3xy^{2} − 6y^{3}

Factorize each of the following expression:

abx^{2} + (ay − b) x − y

Factorize each of the following expression:

(ax + by)^{2} + (bx − ay)^{2}

Factorize each of the following expression:

16(a − b)^{3} − 24 (a − b)^{2}

Factorize each of the following expression:

ab(x^{2} + 1) + x(a^{2} + b^{2})

Factorize each of the following expression:

a^{2}x^{2} + (ax^{2} + 1)x + a

Factorize each of the following expression:

a(a − 2b − c) + 2bc

Factorize each of the following expression:

a(a + b − c) − bc

Factorize each of the following expression:

x^{2} − 11xy − x + 11y

Factorize each of the following expression:

ab − a − b + 1

Factorize each of the following expression:

x^{2} + y − xy − x

#### RD Sharma solutions for Class 8 Maths Chapter 7 Factorization Exercise 7.5 [Page 17]

Factorize each of the following expression:

16x^{2} − 25y^{2}

Factorize each of the following expression:

27x^{2} − 12y^{2}

Factorize each of the following expression:

144a^{2} − 289b^{2}

Factorize each of the following expression:

12m^{2} − 27

Factorize each of the following expression:

125x^{2} − 45y^{2}

Factorize each of the following expression:

144a^{2} − 169b^{2}

Factorize each of the following expression:

(2a − b)^{2} − 16c^{2}

Factorize each of the following expression:

(x + 2y)^{2} − 4(2x − y)^{2}

Factorize each of the following expression:

3a^{5} − 48a^{3}

Factorize each of the following expression:

a^{4} − 16b^{4}

Factorize each of the following expression:

x^{8} − 1

Factorize each of the following expression:

64 − (a + 1)^{2}

Factorize each of the following expression:

36l^{2} − (m + n)^{2}

Factorize each of the following expression:

25x^{4}y^{4} − 1

Factorize each of the following expression:

Factorize each of the following expression:

x^{3} − 144x

Factorize each of the following expression:

(x - 4y)^{2} − 625

Factorize each of the following expression:

9(a − b)^{2} − 100(x − y)^{2}

Factorize each of the following expression:

(3 + 2a)^{2} − 25a^{2}

Factorize each of the following expression:

(x + y)^{2} − (a − b)^{2}

Factorize each of the following expression:

\[\frac{1}{16} x^2 y^2 - \frac{4}{49} y^2 z^2\]

Factorize each of the following expression:

75a^{3}b^{2} - 108ab^{4}

Factorize each of the following expression:

x^{5} − 16x^{3}

Factorize each of the following expression:

Factorize each of the following expression:

256x^{5} − 81x

Factorize each of the following expression:

a^{4} − (2b + c)^{4}

Factorize each of the following expression:

(3x + 4y)^{4} − x^{4}

Factorize each of the following expression:

p^{2}q^{2} − p^{4}q^{4}

Factorize each of the following expression:

3x^{3}y − 243xy^{3}

Factorize each of the following expression:

a^{4}b^{4}^{ }− 16c^{4}

Factorize each of the following expression:

x^{4} − 625

Factorize each of the following expression:

x^{4} − 1

Factorize each of the following expression:

49(a − b)^{2} − 25(a + b)^{2}

Factorize each of the following expression:

x − y − x^{2} + y^{2}

Factorize each of the following expression:

16(2x − 1)^{2} − 25y^{2}

Factorize each of the following expression:

4(xy + 1)^{2} − 9(x − 1)^{2}

Factorize each of the following expression:

(2x + 1)^{2} − 9x^{4}

Factorize each of the following expression:

x^{4} − (2y − 3z)^{2}

*Factorize each of the following expression:**a*^{2} − *b*^{2} + *a − b*

Factorize each of the following expression:

16a^{4} − b^{4}

Factorize each of the following expression:

a^{4} − 16(b − c)^{4}

Factorize each of the following expression:

2a^{5} − 32a

Factorize each of the following expression:

a^{4}b^{4} − 81c^{4}

Factorize each of the following expression:

xy^{9} − yx^{9}

Factorize each of the following expression:

x^{3} − x

Factorize each of the following expression:

18a^{2}x^{2} − 32

#### RD Sharma solutions for Class 8 Maths Chapter 7 Factorization Exercise 7.6 [Pages 22 - 23]

Factorize each of the following algebraic expression:

4x^{2}^{ }+ 12xy +9y^{2}

Factorize each of the following algebraic expression:

9a^{2} − 24ab + 16b^{2}

Factorize each of the following algebraic expression:

p^{2}q^{2} − 6pqr + 9r^{2}

Factorize each of the following algebraic expression:

36a^{2} + 36a + 9

Factorize each of the following algebraic expression:

a^{2} + 2ab + b^{2} − 16

Factorize each of the following algebraic expression:

9z^{2} − x^{2} + 4xy − 4y^{2}

Factorize each of the following algebraic expression:

9a^{4} − 24a^{2}b^{2} + 16b^{4} − 256

Factorize each of the following algebraic expression:

16 − a^{6} + 4a^{3}b^{3} − 4b^{6}

Factorize each of the following algebraic expression:

a^{2} − 2ab + b^{2} − c^{2}

Factorize each of the following algebraic expression:

x^{2} + 2x + 1 − 9y^{2}

Factorize each of the following algebraic expression:

a^{2} + 4ab + 3b^{2}

Factorize each of the following algebraic expression:

96 − 4x − x^{2}

Factorize each of the following algebraic expression:

a^{4} + 3a^{2} +4

Factorize each of the following algebraic expression:

4x^{4} + 1

Factorize each of the following algebraic expression:

4x^{4} + y^{4}

Factorize each of the following algebraic expression:

(x + 2)^{2} − 6(x + 2) + 9

Factorize each of the following algebraic expression:

25 − p^{2} − q^{2} − 2pq

Factorize each of the following algebraic expression:

x^{2} + 9y^{2} − 6xy − 25a^{2}

Factorize each of the following algebraic expression:

49 − a^{2} + 8ab − 16b^{2}

Factorize each of the following algebraic expression:

a^{2} − 8ab + 16b^{2} − 25c^{2}

Factorize each of the following algebraic expression:

x^{2} − y^{2} + 6y − 9

Factorize each of the following algebraic expression:

25x^{2} − 10x + 1 − 36y^{2}

Factorize each of the following algebraic expression:

a^{2} − b^{2} + 2bc − c^{2}

Factorize each of the following algebraic expression:

a^{2} + 2ab + b^{2} − c^{2}

Factorize each of the following algebraic expression:

49 − x^{2} − y^{2} + 2xy

Factorize each of the following algebraic expression:

a^{2} + 4b^{2} − 4ab − 4c^{2}

Factorize each of the following algebraic expression:

x^{2} − y^{2} − 4xz + 4z^{2}

#### RD Sharma solutions for Class 8 Maths Chapter 7 Factorization Exercise 7.7 [Page 27]

Factorize each of the following algebraic expression:

x^{2} + 12x − 45

Factorize each of the following algebraic expression:

40 + 3x − x^{2}

Factorize each of the following algebraic expression:

a^{2} + 3a − 88

Factorize each of the following algebraic expression:

a^{2} − 14a − 51

Factorize each of the following algebraic expression:

x^{2} + 14x + 45

Factorize each of the following algebraic expression:

x^{2} − 22x + 120

Factorize each of the following algebraic expression:

x^{2} − 11x − 42

Factorize each of the following algebraic expression:

a^{2} + 2a − 3

Factorize each of the following algebraic expression:

a^{2} + 14a + 48

Factorize each of the following algebraic expression:

x^{2} − 4x − 21

Factorize each of the following algebraic expression:

y^{2} + 5y − 36

Factorize each of the following algebraic expression:

(a^{2} − 5a)^{2} − 36

Factorize each of the following algebraic expression:

(a + 7)(a − 10) + 16

#### RD Sharma solutions for Class 8 Maths Chapter 7 Factorization Exercise 7.9 [Pages 32 - 33]

Factorize each of the following quadratic polynomials by using the method of completing the square:

p^{2} + 6p + 8

Factorize each of the following quadratic polynomials by using the method of completing the square:

q2 − 10q + 21

Factorize each of the following quadratic polynomials by using the method of completing the square:

4y^{2} + 12y + 5

Factorize each of the following quadratic polynomials by using the method of completing the square:

p^{2} + 6p − 16

Factorize each of the following quadratic polynomials by using the method of completing the square:

x^{2} + 12x + 20

Factorize each of the following quadratic polynomials by using the method of completing the square:

a^{2} − 14a − 51

Factorize each of the following quadratic polynomials by using the method of completing the square:

a^{2} + 2a − 3

Factorize each of the following quadratic polynomials by using the method of completing the square:

4x^{2} − 12x + 5

Factorize each of the following quadratic polynomials by using the method of completing the square:

y^{2} − 7y + 12

Factorize each of the following quadratic polynomials by using the method of completing the square:

z^{2} − 4z − 12

## Chapter 7: Factorization

## RD Sharma solutions for Class 8 Maths 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 Class 8 Maths 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 Maths 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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