#### 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

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

## Chapter 7: Factorization

#### Chapter 7: Factorization Exercise 7.10 solutions [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}

#### Chapter 7: Factorization Exercise 7.20 solutions [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

#### Chapter 7: Factorization Exercise 7.30 solutions [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)

#### Chapter 7: Factorization Exercise 7.40 solutions [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

#### Chapter 7: Factorization Exercise 7.50 solutions [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

#### Chapter 7: Factorization Exercise 7.60 solutions [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}

#### Chapter 7: Factorization Exercise 7.70 solutions [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

#### Chapter 7: Factorization Exercise 7.90 solutions [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 Mathematics Class 8 by R D Sharma (2019-2020 Session)

#### Textbook solutions for Class 8

## 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.

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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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