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Chapters
1: Rational and Irrational Numbers
UNIT-II: COMMERCIAL MATHEMATICS
2: Compound Interest
UNIT-III: ALGEBRA
3: Expansions
▶ 4: Factorisation
5: Simultaneous Linear Equations
6: Indices
7: Logarithms
UNIT-IV: GEOMETRY
8: Triangles
9: Inequalities
10: Mid-point Theorem
11: Pythagoras Theorem
12: Rectilinear Figures (Theorems on Parallelograms and Construction of Polygons)
13: Theorems on Area
14: Circles (Chord and Arc Properties)
UNIT-V: STATISTICS
15: Statistics
16: Graphical Representation of Statistical Data
UNIT-VI: MENSURATION
17: Mensuration
18: Surface Area and Volume of Solids
UNIT-VII: TRIGONOMETRY
19: Trigonometry
20: Simple 2-D Problems in Right Triangle
UNIT-VIII: COORDINATE GEOMETRY
21: Coordinate Geometry
![B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE chapter 4 - Factorisation - Shaalaa.com](/images/mathematics-english-class-9-icse_6:a927b361d63845f4b2afea4ec6bbe35a.jpg "B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE chapter 4 - Factorisation")
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Solutions for Chapter 4: Factorisation
Below listed, you can find solutions for Chapter 4 of CISCE B Nirmala Shastry for Mathematics [English] Class 9 ICSE.
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 4 Factorisation EXERCISE 4A [Page 42]
Factorise the following:
12a2b – 16ab2 – 28a2b2
Factorise the following:
7a2x – 7x + a2p – p
Factorise the following:
c2d – c2 – 4d + 4
Factorise the following:
a2x – a2y – 9x + 9y
Factorise the following:
2a3 – a2 – 8a + 4
Factorise the following:
5a – b + x(b – 5a)
Factorise the following:
(2c – d) – a(d – 2c)
Factorise the following:
b(x – y) – 3(y – x) + a(y – x)
Factorise the following:
3a2 – 6a – ka + 2k + am – 2m
Factorise:
a2 – ab(1 – b) – b3
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 4 Factorisation EXERCISE 4B [Page 43]
Factorise the following:
49x2 – 64y2
Factorise the following:
121x2 – 169y2
Factorise the following:
72x2 – 50y2
Factorise the following:
80y3 – 5y
Factorise the following:
75a2b2 – 108c2
Factorise the following:
18ab3 – 8a3b
Factorise the following:
(x + 3)(x – 3) – 40
Factorise the following:
(x + 2) (x – 2) – 60
Factorise the following:
`(x + 1)(x - 1) - 5/4`
Factorise the following:
16a4 – 81b4
Factorise the following:
625a4 – 256b4
Factorise the following:
`x^4 - 1/x^4`
Factorise the following:
`x^8 - 1/x^8`
Factorise the following:
256x8 – y8
Factorise the following:
`a^4 - 1/81`
Factorise the following:
(a + 8)2 – (b + 5)2
Factorise the following:
36(a + 3)2 – 25(a – 2)2
Factorise the following:
49(2x + y)2 – 64(x – 2y)2
Factorise the following:
9x2 – 4(y + 2x)2
Factorise the following:
36 – (a + 2b)2
Factorise the following:
`(x - y/3)^2 - (49y^2)/9`
Factorise the following:
4c2 – a2 – 2ab – b2
Factorise the following:
9a2 – b2 + 2bc – c2
Factorise the following:
a2 – 9b2 + 6b – 1
Factorise the following:
25 – a2 + 2ab – b2
Factorise the following:
49x2 – 25y2 + 10y – 1
Factorise the following:
16a2 – 9b2 + 30bc – 25c2
Factorise the following:
a2 + b2 – c2 – d2 + 2ab – 2cd
Factorise the following:
1 + x2y2 + 4xy – x2 – y2
Factorise the following:
a2 – 16 + ab + 4b
Factorise the following:
a2 – 25 – ab + 5b
Factorise the following:
x2 – 4 – 3xy + 6y
Factorise the following:
x2 – 36 – 7xy + 42y
Factorise the following:
x3 – 3x2 – x + 3
Factorise the following:
x3 – 5x2 – 4x + 20
Factorise the following:
(x2 – 4)2 – 9x2
Factorise the following:
(x2 + y2 – z2)2 – 4x2y2
Factorise the following:
(a2 + 4b2 – c2)2 – 16a2b2
Find the value using algebraic formula.
124 × 126
Find the value using algebraic formula.
8.952 – 1.052
Find the value using algebraic formula.
99982 – 9999 × 9997
Find the value using algebraic formula.
`(99813 xx 99815 + 1)/(99814)^2`
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 4 Factorisation EXERCISE 4C [Pages 44 - 45]
Factorise the following:
a2 – 3a – 54
Factorise the following:
a2 – 25a + 84
Factorise the following:
1 – 18a – 63a2
Factorise the following:
x2 – 10x – 24
Factorise the following:
x2 – x – 6
Factorise the following:
x2 – 5x + 6
Factorise the following:
3x2 – 2x – 16
Factorise the following:
5x2 – 13x – 6
Factorise the following:
10x2 + 7x – 12
Factorise the following:
3x2 – 5x – 12
Factorise the following:
5x2 – 17x – 12
Factorise the following:
2x2 – 7x – 39
Factorise the following:
6x2 – x – 12
Factorise the following:
2x2 – 3x – 65
Factorise the following:
4x2 – 8x – 21
Factorise the following:
5a2 – 10a – 15
Factorise the following:
4a2 – 12a – 216
Factorise the following:
3x2 – 15x – 18
Factorise by substituting terms:
12(a + b)2 – 5(a + b) – 3
Factorise by substituting terms:
3(x – y)2 – 4x + 4y – 4
Factorise by substituting terms:
(2x – y)2 – 14x + 7y – 18
Factorise by substituting terms:
6(x + 2)2 – 5(x + 2) – 4
Factorise by substituting terms:
5(x + y)2 – 6x – 6y – 8
Factorise by substituting terms:
(a2 – 2a)2 – 18(a2 – 2a) + 45
Write the following as a product of factor:
x(3x – 11) + 6
Write the following as a product of factor:
x(2x + 1) – 6
Write the following as a product of factor:
x(2x + 5) – 25
Write the following as a product of factor:
x(2x + 5) – 3
Factorise by splitting the middle term to get two perfect squares.
x4 + 3x2 + 4
Factorise by splitting the middle term to get two perfect squares.
x4 + 5x2 + 9
Factorise by splitting the middle term to get two perfect squares.
x4 – 5x2 + 4
Factorise by splitting the middle term to get two perfect squares.
x4 – 10x2 + 9
Factorise by splitting the middle term to get two perfect squares.
a4 – 7a2b2 + b4
Factorise by splitting the middle term to get two perfect squares.
a4 + 2a2b2 + 9b4
Factorise by splitting the middle term to get two perfect squares.
a4 + a2b2 + 25b4
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 4 Factorisation EXERCISE 4D [Page 46]
Factorise:
8x3 + 343y3
Factorise:
64a3 + 125b3
Factorise:
`216a^3 + b^3/343`
Factorise:
`a^3 + 1/(27a^3)`
Factorise:
a3 – 8b3
Factorise:
125a3 – 27b3
Factorise:
343a3 – 216b3
Factorise:
`x^3 - y^3/1331`
Factorise:
x5 + 1728x2
Factorise:
8a4 + 27a
Factorise:
x2 – 8x5
Factorise:
a6 – b6
Factorise:
a6 – 64b6
Factorise:
64a6 – 729b6
Factorise:
15625a6 – 64b6
Factorise:
3a7 – 192ab6
Evaluate using algebraic formula:
`((0.68)^3 - (0.13)^3)/((0.68)^2 + (0.68 xx 0.13) + (0.13)^2`
Evaluate using algebraic formula:
`((0.78)^3 + (0.22)^3)/((0.78)^2 - (0.78 xx 0.22) + (0.22)^2)`
Factorise:
x4 + x3 + 27x + 27
Factorise:
x4 – x3 – 8x + 8
Factorise:
8x3 + 27y3 + 10x + 15y
Factorise:
x3 + 125y3 + 2x + 10y
Factorise:
x3 – 216y3 – 3x + 18y
Factorise:
x3 – 8y3 – 6x + 12y
Factorise:
x6 – 7x3 – 8
Factorise:
x6 + 26x3 – 27
Factorise:
x6 – 124x3 – 125
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 4 Factorisation MULTIPLE CHOICE QUESTIONS [Pages 46 - 47]
9x2 – 36y2 is equal to ______.
(3x + 6y) (3x – 6y)
(3x – 6y)2
9(x + 2y) (x – 2y)
9(x – 6y)2
x(x – y) + 5(y – x) is equal to ______.
(x – y) (x + 5)
(x – y) (5 – x)
(x – y) (x – 5)
(x + y) (x – 5)
10xy – 4y – 6 + 15x is equal to ______.
(2y – 3) (5x + 2)
(5x – 2) (2y + 3)
(2 – 5x) (2y + 3)
(2x – 5) (3y – 2)
28x2 – 7y2 is equal to ______.
7(x + 4y) (x – 4y)
7(4x + y) (4x – y)
7(2x + y) (2x – y)
7(x + y) (x – y)
x4 – 16y4 is equal to ______.
(x2 – 4y2)2
(x2 + 4y2) (x2 – 4y2)
(x + 2y)2 (x – 2y)2
(x2 + 4y2) (x + 2y) (x – 2y)
x2 – 15x – 54 is equal to ______.
(x – 9) (x – 6)
(x – 9) (x + 6)
(x – 18) (x + 3)
(x + 18) (x – 3)
x2 – 5x + 6 is equal to ______.
(x + 2) (x + 3)
(x – 6) (x + 1)
(x – 1) (x + 6)
(x – 2) (x – 3)
9x2 + 6x + 1 is equal to ______.
(3x + 1) (3x – 1)
(x + 3) (9x + 1)
(9x + 3) (x + 1)
(3x + 1) (3x + 1)
x2 – 10x + 24 is equal to ______.
(x – 6) (x – 4)
(x – 12) (x + 2)
(x + 6) (x – 4)
(x + 12) (x – 2)
2x2 – x – 15 is equal to ______.
(2x – 3) (x + 5)
(2x + 3) (x – 5)
(x – 3) (2x + 5)
(x + 3) (2x – 5)
x2 – 8x + 12 is equal to ______.
(x – 4) (x – 3)
(x – 6) (x + 2)
(x + 4) (x + 3)
(x – 6) (x – 2)
3x2 + 2x – 8 is equal to ______.
(3x + 4) (x – 2)
(3x – 4) (x + 2)
(3x – 8) (x + 1)
(3x + 8) (x – 1)
`8x^3 - 27/y^3` is equal to ______.
`(2x - 3/y)(4x^2 + 6xy + 9/y^2)`
`(2x + 3/y)(4x^2 - (6x)/y + 9/y^2)`
`(2x - 3/y)(4x^2 + (6x)/y - 9/y^2)`
`(2x - 3/y)(4x^2 + (6x)/y - 9/y^2)`
x – 8x4 is equal to ______.
(x – 2x2) (x + 4x2)
(x + 2x2) (1 – 4x2)
x(1 – 2x) (1 + 2x + 4x2)
x(1 + 2x) (1 – 2x + 4x2)
`(77 xx 77 xx 77 + 23 xx 23 xx 23)/(77 xx 77 - 77 xx 23 + 23 xx 23)` is equal to ______.
90
100
110
120
`(74 xx 74 - 16 xx 16)/(74 + 16)` is equal to ______.
90
100
58
68
`(203^2 - 197^2)/400` is equal to ______.
3
4
5
6
x3 + 27y3 is equal to ______.
(x + 3y)3
(x + 3y) (x2 – 6xy + 9y2)
(x + 3y) (x2 – 3xy + 9y2)
(x + 3y) (x2 + 3xy + 9y2)
Assertion: x3 + 8y3 = (x + 2y) (x2 – 2xy + 4y2).
Reason: a3 – b3 = (a – b) (a2 + ab + b2).
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: y2 + y – 6 = (y + 3) (y – 2)
Reason: 3y – 2y = y and 3y × (–2y) = –6y2
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: x3 – 5x2 – x + 5 = (x – 5) (x + 1) (x – 1).
Reason: a2 – b2 = (a + b) (a – b).
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: 732 – 722 = 145.
Reason: 732 – 722 = (73 + 72) (73 – 72) = 145 × 1.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: The factors of x2 – 10x – 24 = (x – 4) (x – 6).
Reason: A trinomial of the form ax2 + bx + c can be factorised if b2 – 4ac is a perfect square.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: x – 64x4 = x(1 + 8x2) (1 – 8x2)
Reason: a2 – b2 = (a + b) (a – b)
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 4 Factorisation MISCELLANEOUS EXERCISE [Page 48]
Factorise:
25(a + b)2 – 36(a – b)2
Factorise:
(y2 + 3)2 – 16y2
Factorise:
5x4 – 80y4
Factorise:
27a2b – 75b3
Factorise the following:
5x2 – 5x – 30
Factorise the following:
x2 – 15xy – 54y2
Factorise the following:
6x2 – 15x – 9
Factorise the following:
3(x – 2y)2 + 4(x – 2y) – 15
Factorise the following:
a4 + 4b4 – 5a2b2
Factorise the following:
x4 – 13x2 + 36
Factorise:
`8x^3 − y^3/343`
Factorise:
`a^3/27 + 8/b^3`
Factorise:
a6 – 15625b6
Factorise:
729a6 – b6
Factorise:
a2 – 4b2 + a3 – 8b3 – (a – 2b)2
Factorise:
a3 – 216b3 – 7a + 42b
Find the value of (using algebraic formula):
`((743)^3 − (543)^3)/((743)^2 + (743)(543) + (543)^2)`
The area of a rectangle is (14x2 – 29xy – 15y2) sq units. Find its sides and the perimeter of the rectangle.
Factorise:
9b2 – 4a2 + 20a – 25
Factorise:
4 – x2 + 10xy – 25y2
Factorise:
36a2 – b2 + 20bc – 100c2
Factorise:
49a2 – 25b2 + 60bc – 36c2
Factorise:
x3 – 5x2 – 9x + 45
Factorise:
x3 – 3x2 – 4x + 12
Factorise:
7xy2 – 7x + 2y2 – 2
Factorise the following:
c2d – c2 – 4d + 4
Show that 101 is a factor of 873 + 143.
Solutions for 4: Factorisation
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE chapter 4 - Factorisation
Shaalaa.com has the CISCE Mathematics Mathematics [English] Class 9 ICSE CISCE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. B Nirmala Shastry solutions for Mathematics Mathematics [English] Class 9 ICSE CISCE 4 (Factorisation) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. B Nirmala Shastry textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in Mathematics [English] Class 9 ICSE chapter 4 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 B Nirmala Shastry Mathematics [English] Class 9 ICSE solutions Factorisation exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in B Nirmala Shastry Solutions are essential questions that can be asked in the final exam. Maximum CISCE Mathematics [English] Class 9 ICSE students prefer B Nirmala Shastry Textbook Solutions to score more in exams.
Get the free view of Chapter 4, Factorisation Mathematics [English] Class 9 ICSE additional questions for Mathematics Mathematics [English] Class 9 ICSE CISCE, and you can use Shaalaa.com to keep it handy for your exam preparation.
