Chapters
Chapter 2: Exponents of Real Numbers
Chapter 3: Rationalisation
Chapter 4: Algebraic Identities
Chapter 5: Factorisation of Algebraic Expressions
Chapter 6: Factorisation of Polynomials
Chapter 7: Linear Equations in Two Variables
Chapter 8: Co-ordinate Geometry
Chapter 9: Introduction to Euclid’s Geometry
Chapter 10: Lines and Angles
Chapter 11: Triangle and its Angles
Chapter 12: Congruent Triangles
Chapter 13: Quadrilaterals
Chapter 14: Areas of Parallelograms and Triangles
Chapter 15: Circles
Chapter 16: Constructions
Chapter 17: Heron’s Formula
Chapter 18: Surface Areas and Volume of a Cuboid and Cube
Chapter 19: Surface Areas and Volume of a Circular Cylinder
Chapter 20: Surface Areas and Volume of A Right Circular Cone
Chapter 21: Surface Areas and Volume of a Sphere
Chapter 22: Tabular Representation of Statistical Data
Chapter 23: Graphical Representation of Statistical Data
Chapter 24: Measures of Central Tendency
Chapter 25: Probability
Chapter 5: Factorisation of Algebraic Expressions
RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.1 [Page 9]
Factorize: x3 + x - 3x2 - 3
Factorize: a (a + b)3 - 3a2b (a + b)
Factorize x (x3 - y3 ) + 3xy ( x - y )
Factorize: `a^2 x^2 + (ax^2 + 1)x + a`
Factorize : x2 + y - xy - x
Factorize x3 - 2x2 y + 3xy2 - 6y3
Factorize `6ab - b^2 + 12ac - 2bc`
Factorize x( x - 2)( x - 4) + 4x - 8
Factorize (a - b + c)2 + (b - c + a)2 + 2(a - b + c) (b - c + a)
Factorize a2 + 2ab + b2 - c2
Factorize a2 + 4b2 - 4ab - 4c2
Factorize x2 - y2 - 4xz + 4z2
Factorize `2x^2 - 5/6x + 1/12`
Factorize `x^2 + 12/35 x + 1/35`
Factorize `21x^2 - 2x + 1/21`
Given possible expressions for the length and breadth of the rectangle having 35y2 + 13y – 12 as its area.
What are the possible expressions for the dimensions of the cuboid whose volume is 3x2 - 12x.
Factorize `[x^2 + 1/x^2] - 4[x + 1/x] + 6`
Factorize (x + 2)(x2 + 25) -10x2 - 20x
Factorize `2a^2 + 2 sqrt6ab + 3b^2`
Factorize: a2 + b2 + 2 (ab + bc + ca)
Factorize 4( x - y)2 -12( x - y)( x + y ) + 9(x + y )2
Factorize a2 - b2 + 2bc - c2
Factorize xy9 - yx9
Factorize x4 + x2 y2 + y4
Factorize `x^2 + 6sqrt2x + 10`
Factorize `x^2 - 2sqrt2x - 30`
Factorize `x^2 - sqrt3x - 6`
Factorize `x^2 + 5sqrt5x + 30`
Factorize `x^2 + 2sqrt3x - 24`
Factorize `5sqrt5x^2 + 20x + 3sqrt5`
Factorize `2x^2 + 3sqrt5x + 5`
Factorize `9(2a - b)^2 - 4(2a - b) - 13`
Factorize `7(x - 2y)^2 - 25(x - 2y) + 12`
Factorize 2( x + y)2 - 9( x + y) - 5
RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.2 [Page 14]
Factorize the following expressions:
p3 + 27
Factorize the following expressions:
y3 +125
Factorize the following expressions
1- 27a3
Factorize the following expressions
8x3 y3 + 27a3
Factorize the following expressions
64a3 – b3
Factorize the following expressions:
`x^3/216 - 8y^3`
Factorize the following expressions:
10x4y – 10xy4
Factorize the following expressions:
54x6y + 2x3y4
Factorize the following expressions:
32a3 + 108b3
Factorize the following expressions:
(a - 2b)3 - 512b3
Factorize the following expressions:
`8x^2y^3 - x^5`
Factorize the following expressions:
1029 – 3x3
Factorize the following expressions:
x3y3 + 1
Factorize the following expressions:
x4y4 - xy
Factorize the following expressions:
a3 + b3 + a + b
Simplify `(173 xx 173 xx 173 xx 127 xx 127 xx 127)/(173 xx 173 xx 173 xx 127 xx 127 xx 127)`
Simplify `(155 xx 155 xx 155 - 55 xx 55 xx 55)/(155 xx 155 + 155 xx 55 + 55 xx 55)`
Simplify : \[\frac{1 . 2 \times 1 . 2 \times 1 . 2 - 0 . 2 \times 0 . 2 \times 0 . 2}{1 . 2 \times 1 . 2 + 1 . 2 \times 0 . 2 + 0 . 2 \times 0 . 2}\]
Factorize the following expressions:
(a + b)3 – 8(a – b)3
Factorize the following expressions:
( x + 2)3 + ( x - 2)3
Factorize the following expressions:
x6 + y6
Factorize the following expressions:
a12 + b12
Factorize the following expressions:
x3 + 6x2 +12x +16
Factorize the following expressions:
`a^3 - 1/a^3 - 2a + 2/a`
Factorize the following expressions:
a3 + 3a2b + 3ab2 + b3 - 8
Factorize the following expressions:
8a3 - b3 - 4ax + 2bx
RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.3 [Page 17]
Factorize 64a3 +125b3 + 240a2b + 300ab2
Factorize 125x3 - 27 y3 - 225x2 y +135xy2
Factorize `8/27 x^3 + 1 + 4/3 x^2 + 2x`
Factorize 8x3 + 27 y3 + 36x2 y + 54xy2
Factorize a3 – 3a2b + 3ab2 – b3 + 8
Factorize x3 + 8y3 + 6x2 y +12xy2
Factorize 8x2 + y3 +12x2 y + 6xy2
Factorize 8a3 + 27b3 + 36a2b + 54ab2
Factorize 8a3 – 27b3 – 36a2b + 54ab2
Factorize x3 -12x ( x - 4) - 64
Factorize a3 x3 - 3a2bx2 + 3ab2 x - b3
RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.4 [Page 23]
a3 + 8b3 + 64c3 - 24abc
x3 - 8y3 + 27z3 +18xyz
27x3 − y3 − z3 − 9xyz
`1/27 x^3 - y^3 + 125z^3 + 5xyz`
8x3 + 27y3 - 216z3 + 108xyz
125 + 8x3 - 27 y3 + 90xy
8x3 -125y3 +180xy + 216
Multiply: x2 + y2 + z2 − xy + xz + yz by x + y − z
Multiply: x2 + 4y2 + z3 + 2xy + xz − 2yz by x − 2y − z
Multiply: x2 + 4y2 + 2xy − 3x + 6y + 9 by x − 2y + 3
Multiply: 9x2 + 25y2 + 15xy + 12x − 20y + 16 by 3x − 5y + 4
(3x - 2 y)3 + (2 y - 4z )3 + (4z - 3x)3
(2x - 3y)3 + (4z - 2x)3 + (3y - 4z )3
`(x/2 + y + z/3)^3 + (x/2 + (2y)/3 + z)^3 + (-(5x)/6 - y/3 - (4z)/3)^3`
(a – 3b)3 + (3b – c)3 + (c – a)3
`2sqrt2a^3 + 3sqrt3b^3 + c^3 - 3 sqrt6abc`
`3sqrt3a^3 - b^3 - 5sqrt5c^3 - 3sqrt15abc`
`2sqrt2a^3 + 16sqrt2b^3 + c^3 - 12abc`
Find the value of x3 + y3 − 12xy + 64, when x + y =−4
RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions [Pages 24 - 25]
If a + b + c = 0, then write the value of a3 + b3 + c3.
If a2 + b2 + c2 = 20 and a + b + c = 0, find ab + bc + ca.
If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 +c2.
If a2 + b2 + c2 = 250 and ab + bc + ca = 3, find a + b + c.
Write the value of 253 − 753 + 503.
Write the value of 483 − 303 − 183.
Write the value of \[\left( \frac{1}{2} \right)^3 + \left( \frac{1}{3} \right)^3 - \left( \frac{5}{6} \right)^3 .\]
Write the value of 303 + 203 − 503.
Factorize: x4 + x2 + 25.
Factorize : x2 − 1 − 2a − a2
RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions [Pages 25 - 26]
The factors of x3 −x2y − xy2 + y3 are
(x + y) (x2 − xy + y2)
(x + y) (x2 + xy + y2)
(x + y)2 (x − y)
(x − y)2 (x + y)
The factors of x3 − 1 + y3 + 3xy are
(x − 1 + y) (x2 + 1 + y2 + x + y − xy)
(x + y + 1) (x2 + y2 + 1 −xy − x − y)
(x − 1 + y) (x2 − 1 − y2 + x + y + xy)
3(x + y −1) (x2 + y2 − 1)
The factors of 8a3 + b3 − 6ab + 1 are
(2a + b − 1) (4a2 + b2 + 1 − 3ab − 2a)
(2a − b + 1) (4a2 + b2 − 4ab + 1 − 2a + b)
(2a + b + 1) (4a2 + b2 + 1 −2ab − b − 2a)
(2a − 1 + b) (4a2 + 1 − 4a − b − 2ab)
(x + y)3 − (x − y)3 can be factorized as
2y (3x2 + y2)
2x (3x2 + y2)
2y (3y2 + x2)
2x (x2+ 3y2)
The expression (a − b)3 + (b − c)3 + (c −a)3 can be factorized as
(a − b) (b − c) (c −a)
3(a − b) (b − c) (c −a)
−3(a − b) (b −c) (c − a)
(a + b + c) (a2 + b2 + c2 − ab − bc − ca)
The value of \[\frac{(2 . 3 )^3 - 0 . 027}{(2 . 3 )^2 + 0 . 69 + 0 . 09}\]
2
3
2.327
2.273
The value of \[\frac{(0 . 013 )^3 + (0 . 007 )^3}{(0 . 013 )^2 - 0 . 013 \times 0 . 007 + (0 . 007 )^2}\] is
0.006
0.02
0.0091
0.00185
Mark the correct alternative in each of the following: The factors of a2 − 1 − 2x − x2 are
(a − x + 1) (a − x − 1)
(a + x − 1) (a − x + 1)
` (a+x+1)(a- x -1)`
none of these
The factors of x4 + x2 + 25 are
(x2 + 3x + 5) (x2 − 3x + 5)
(x2 + 3x + 5) (x2 + 3x − 5)
(x2 + x +5) (x2 − x + 5)
none of these
The factors of x2 + 4y2 + 4y − 4xy − 2x − 8 are
(x − 2y −4) (x − 2y + 2)
(x − y + 2) (x − 4y − 4)
(x + 2y − 4) (x + 2y + 2)
none of these
The factors of x3 − 7x + 6 are
x (x − 6) (x − 1)
(x2 − 6) (x − 1)
(x + 1) (x + 2) (x + 3)
(x − 1) (x + 3) (x − 2)
The expression x4 + 4 can be factorized as
(x2 + 2x + 2) (x2 − 2x + 2)
(x2 + 2x + 2) (x2 + 2x + 2)
(x2 − 2x − 2) (x2 − 2x + 2)
(x2 + 2) (x2 − 2)
If 3x = a + b + c, then the value of (x − a)3 + (x −b)3 + (x − c)3 − 3(x − a) (x − b) (x −c) is
a + b + c
(a − b) (b − c) (c − a)
0
none of these
If (x + y)3 − (x − y)3 − 6y(x2 − y2) = ky2, then k =
1
2
4
8
If x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c), then a + b + c =
4
12
-10
3
Chapter 5: Factorisation of Algebraic Expressions
RD Sharma solutions for Mathematics for Class 9 chapter 5 - Factorisation of Algebraic Expressions
RD Sharma solutions for Mathematics for Class 9 chapter 5 (Factorisation of Algebraic Expressions) 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 9 solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Mathematics for Class 9 chapter 5 Factorisation of Algebraic Expressions are Concept of Algebraic Expressions.
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