#### Chapters

Chapter 2: Profit , Loss and Discount

Chapter 3: Compound Interest

Chapter 4: Expansions

Chapter 5: Factorisation

Chapter 6: Changing the subject of a formula

Chapter 7: Linear Equations

Chapter 8: Simultaneous Linear Equations

Chapter 9: Indices

Chapter 10: Logarithms

Chapter 11: Triangles and their congruency

Chapter 12: Isosceles Triangle

Chapter 13: Inequalities in Triangles

Chapter 14: Constructions of Triangles

Chapter 15: Mid-point and Intercept Theorems

Chapter 16: Similarity

Chapter 17: Pythagoras Theorem

Chapter 18: Rectilinear Figures

Chapter 19: Quadrilaterals

Chapter 20: Constructions of Quadrilaterals

Chapter 21: Areas Theorems on Parallelograms

Chapter 22: Statistics

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Perimeter and Area

Chapter 25: Surface Areas and Volume of Solids

Chapter 26: Trigonometrical Ratios

Chapter 27: Trigonometrical Ratios of Standard Angles

Chapter 28: Coordinate Geometry

## Chapter 5: Factorisation

### Frank solutions for Class 9 Maths ICSE Chapter 5 Factorisation Exercise 5.1

Factorise the following by taking out the common factors:

4x^{2}y^{3} - 6x^{3}y^{2} - 12xy^{2}

Factorise the following by taking out the common factors:

5a(x^{2} - y^{2}) + 35b(x^{2} - y^{2})

Factorise the following by taking out the common factors:

2x^{5}y + 8x^{3}y^{2} - 12x^{2}y^{3}

Factorise the following by taking out the common factors:

12a^{3 }+ 15a^{2}b - 21ab^{2}

Factorise the following by taking out the common factors:

24m^{4}n^{6} + 56m^{6}n^{4} - 72m^{2}n^{2}

Factorise the following by taking out the common factors:

(a - b)^{2} -2(a - b)

Factorise the following by taking out the common factors:

2a(p^{2} + q^{2}) + 4b(p^{2} + q^{2})

Factorise the following by taking out the common factors:

81(p + q)^{2} -9p - 9q

Factorise the following by taking out the common factors:

(mx + ny)^{2} + (nx - my)^{2}

Factorise the following by taking out the common factors:

36(x + y)^{3} - 54(x + y)^{2}

Factorise the following by taking out the common factors:

p(p^{2} + q^{2} - r^{2}) + q(r^{2} - q^{2} -p^{2}) - r(p^{2} + q^{2} - r^{2})

Factorise the following by grouping the terms:

15xy - 9x - 25y + 15

Factorise the following by grouping the terms:

15x^{2} + 7y - 3x - 35xy

Factorise the following by grouping the terms:

9 + 3xy + x^{2}y + 3x

Factorise the following by grouping the terms:

8(2a + b)^{2} - 8a -4b

Factorise the following by grouping the terms:

x(x - 4)- x + 4

Factorise the following by grouping the terms:

2m^{3} - 5n^{2} - 5m^{2}n + 2mn

Factorise the following by grouping the terms:

4abx^{2} + 49aby^{2} + 14xy(a^{2} + b^{2})

Factorise the following by grouping the terms:

9x^{3} + 6x^{2}y^{2} - 4y^{3} - 6xy

Factorise the following by grouping the terms:

3ax^{2} - 5bx^{2} + 9az^{2} + 6ay^{2} - 10by^{2} - 15bz^{2}

Factorise the following by grouping the terms:

8x^{3} - 24x^{2}y + 54xy^{2} -162y^{3}

Factorise the following by grouping the terms:

2a + b + 3c - d + (2a + b)^{3} + (2a + b)^{2}(3c - d)

Factorise the following by grouping the terms:

xy(a^{2} + 1) + a(x^{2} + y^{2})

Factorise the following by grouping the terms:

p^{2}x^{2} + (px^{2} + 1)x + p

Factorise the following by grouping the terms:

x^{2} - (p + q)x + pq

Factorise the following by grouping the terms:

`"p"^2 + (1)/"p"^2 - 2 - 5"p" + (5)/"p"`

Factorise the following by grouping the terms:

x + y + m(x + y)

Factorise the following by grouping the terms:

`(1)/(25x^2) + 16x^2 + (8)/(5) - 12x - (3)/(5x)`

Factorise the following by grouping the terms:

2p(a^{2} - 2b^{2}) -14p + (a^{2} - 2b^{2})^{2} - 7(a^{2} - 2b^{2})

### Frank solutions for Class 9 Maths ICSE Chapter 5 Factorisation Exercise 5.2

Factorise the following by splitting the middle term:

x^{2} + 6x + 8

Factorise the following by splitting the middle term:

x^{2} - 11x + 24

Factorise the following by splitting the middle term:

x^{2} + 5x - 6

Factorise the following by splitting the middle term:

p^{2}- 12p - 64

Factorise the following by splitting the middle term:

y^{2} - 2y - 24

Factorise the following by splitting the middle term:

3x^{2} + 19x - 14

Factorise the following by splitting the middle term:

15a^{2} - 14a - 16

Factorise the following by splitting the middle term:

12 + x - 6x^{2}

Factorise the following by splitting the middle term:

7x^{2} + 40x - 12

Factorise the following:

5x^{2} - 17xy + 6y^{2}

Factorise the following:

9x^{2} - 22xy + 8y^{2}

Factorise the following:

2x^{3} + 5x^{2}y - 12xy^{2}

Factorise the following:

x^{2}y^{2} + 15xy - 16

Factorise the following:

(2p + q)^{2} - 10p - 5q - 6

Factorise the following:

y^{2} + 3y + 2 + by + 2b

Factorise the following:

x^{3}y^{3} - 8x^{2}y^{2} + 15xy

Factorise the following:

`6sqrt(3)x^2 - 19x + 5sqrt(3)`

Factorise the following:

`2sqrt(5)x^2 - 7x - 3sqrt(5)`

Factorise the following:

5(3x + y)^{2} + 6(3x + y) - 8

Factorise the following:

5 - 4(a - b) - 12(a - b)^{2}

Factorise the following:

(3a - 2b)^{2} +3(3a - 2b) - 10

Factorise the following:

(a^{2} - 2a)^{2} - 23(a^{2} - 2a) + 120

Factorise the following:

(x + 4)^{2} - 5xy - 20y - 6y^{2}

Factorise the following:

7(x - 2)^{2} - 13(x - 2) - 2

Factorise the following:

12 - (y + y^{2})(8 - y - y^{2})

Factorise the following:

(p^{2} + p)^{2} - 8(p^{2} + p) + 12

Factorise the following:

(y^{2} - 3y)(y^{2} - 3y + 7) + 10

Factorise the following:

(t^{2} - t)(4t^{2} - 4t - 5) - 6

Factorise the following:

12(2x - 3y)^{2} - 2x + 3y - 1

Factorise the following:

6 - 5x + 5y + (x - y)^{2}

Factorise the following:

`2x^2 + x/(6) - 1`

Factorise the following:

p^{4} + 23p^{2}q^{2} + 90q^{4}

Factorise the following:

2a^{3} + 5a^{2}b - 12ab^{2}

### Frank solutions for Class 9 Maths ICSE Chapter 5 Factorisation Exercise 5.3

Factorise the following by the difference of two squares:

x^{2} - 16

Factorise the following by the difference of two squares:

64x^{2} - 121y^{2}

Factorise the following by the difference of two squares:

441 - 81y^{2}

Factorise the following by the difference of two squares:

x^{6} - 196

Factorise the following by the difference of two squares:

625 - b^{2}

Factorise the following by the difference of two squares:

`"m"^2 - (1)/(9)"n"^2`

Factorise the following by the difference of two squares:

8xy^{2} - 18x^{3}

Factorise the following by the difference of two squares:

16a^{4} - 81b^{4}

Factorise the following by the difference of two squares:

a(a - 1) - b(b - 1)

Factorise the following by the difference of two squares:

(x + y)^{2} -1

Factorise the following by the difference of two squares:

x^{2} + y^{2} - z^{2} - 2xy

Factorise the following by the difference of two squares:

(x - 2y)^{2} -z^{2}

Factorise the following:

9(a - b)^{2} - (a + b)^{2}

Factorise the following:

25(x - y)^{2} - 49(c - d)^{2}

Factorise the following:

(2a - b)^{2} -9(3c - d)^{2}

Factorise the following:

b^{2} - 2bc + c^{2} - a^{2}

Factorise the following:

`x^2 + (1)/x^2 - 2`

Factorise the following:

(x^{2} + y^{2} - z^{2})^{2} - 4x^{2}y^{2}

Factorise the following:

a^{2} + b^{2} - c^{2} - d^{2} + 2ab - 2cd

Factorise the following:

4xy - x^{2} - 4y^{2} + z^{2}

Factorise the following:

4x^{2} - 12ax - y^{2 }- z^{2} - 2yz + 9a^{2}

Factorise the following:

(x + y)^{3} - x - y

Factorise the following:

y^{4} + y^{2} + 1

Factorise the following:

(a^{2} - b^{2})(c^{2} - d^{2}) - 4abcd

Express each of the following as the difference of two squares:

(x^{2} - 2x + 3)(x^{2} + 2x + 3)

Express each of the following as the difference of two squares:

(x^{2} - 2x + 3) (x^{2} - 2x - 3)

Express each of the following as the difference of two squares:

(x^{2} + 2x - 3) (x^{2} - 2x + 3)

Factorise:

`y^2 + (1)/(4y^2) + 1 - 6y - (3)/y`

Factorise:

`4"a"^2 + (1)/(4"a"^2) - 2 - 6"a" + (3)/(2"a")`

Factorise:

x^{4} + y^{4} - 6x^{2}y^{2}

Factorise:

4x^{4} + 25y^{4} + 19x^{2}y^{2}

Factorise:

`"p"^2 + (1)/"p"^2 - 3`

Factorise:

5x^{2} - y^{2} - 4xy + 3x - 3y

## Chapter 5: Factorisation

## Frank solutions for Class 9 Maths ICSE chapter 5 - Factorisation

Frank solutions for Class 9 Maths ICSE chapter 5 (Factorisation) 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 CISCE Class 9 Maths ICSE 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. Frank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Maths ICSE chapter 5 Factorisation are Factorisation by Taking Out Common Factors, Factorisation by Grouping, Method of Factorisation : Difference of Two Squares, Method of Factorisation : the Sum Or Difference of Two Cubes, Factorisation by Taking Out Common Factors, Factorisation of a Quadratic Trinomial by Splitting the Middle Term, Factorisation by Taking Out Common Factors.

Using Frank Class 9 solutions Factorisation 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 Frank Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 9 prefer Frank Textbook Solutions to score more in exam.

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