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Chapters
2: Exponents of Real Numbers
3: Rationalisation
4: Algebraic Identities
▶ 5: Factorisation of Algebraic Expressions
6: Factorisation of Polynomials
7: Linear Equations in Two Variables
8: Co-ordinate Geometry
9: Introduction to Euclid’s Geometry
10: Lines and Angles
11: Triangle and its Angles
12: Congruent Triangles
13: Quadrilaterals
14: Areas of Parallelograms and Triangles
15: Circles
16: Constructions
17: Heron’s Formula
18: Surface Areas and Volume of a Cuboid and Cube
19: Surface Areas and Volume of a Circular Cylinder
20: Surface Areas and Volume of A Right Circular Cone
21: Surface Areas and Volume of a Sphere
22: Tabular Representation of Statistical Data
23: Graphical Representation of Statistical Data
24: Measures of Central Tendency
25: Probability
![R.D. Sharma solutions for Mathematics [English] Class 9 chapter 5 - Factorisation of Algebraic Expressions - Shaalaa.com](/images/mathematics-english-class-9_6:11020adea10b413d91f3308a8891d691.jpg "R.D. Sharma solutions for Mathematics [English] Class 9 chapter 5 - Factorisation of Algebraic Expressions")
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Solutions for Chapter 5: Factorisation of Algebraic Expressions
Below listed, you can find solutions for Chapter 5 of CBSE R.D. Sharma for Mathematics [English] Class 9.
R.D. Sharma solutions for Mathematics [English] Class 9 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
R.D. Sharma solutions for Mathematics [English] Class 9 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
R.D. Sharma solutions for Mathematics [English] Class 9 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
R.D. Sharma solutions for Mathematics [English] Class 9 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
R.D. Sharma solutions for Mathematics [English] Class 9 5 Factorisation of Algebraic Expressions Exercise 5.5 [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
R.D. Sharma solutions for Mathematics [English] Class 9 5 Factorisation of Algebraic Expressions Exercise 5.6 [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
Solutions for 5: Factorisation of Algebraic Expressions
R.D. Sharma solutions for Mathematics [English] Class 9 chapter 5 - Factorisation of Algebraic Expressions
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Concepts covered in Mathematics [English] Class 9 chapter 5 Factorisation of Algebraic Expressions are Algebraic Expressions.
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