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 4: Algebraic Identities
RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.1 [Pages 6 - 7]
Evaluate the following using identities:
`(2x+ 1/x)^2`
Evaluate the following using identities:
(2x + y) (2x − y)
Evaluate the following using identities:
`(a^2b - b^2a)^2`
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Evaluate the following using identities:
(399)2
Evaluate the following using identities:
(0.98)2
Evaluate following using identities:
991 ☓ 1009
Evaluate the following using identities:
117 x 83
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
Simplify the following products:
`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
if `x^2 + 1/x^2 = 79` Find the value of `x + 1/x`
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
Simplify the following products:
`(x^2 + x - 2)(x^2 - x + 2)`
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Simplify the following products:
`(2x^4 - 4x^2 + 1)(2x^4 - 4x^2 - 1)`
Prove that a2 + b2 + c2 − ab − bc − ca is always non-negative for all values of a, b and c
RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.2 [Pages 11 - 12]
Write in the expanded form:
`(a + 2b + c)^2`
Write in the expanded form:
(2a - 3b - c)2
Write the expanded form:
`(-3x + y + z)^2`
Write in the expanded form:
`(m + 2n - 5p)^2`
Write in the expanded form:
`(2 + x - 2y)^2`
Write in the expanded form (a2 + b2 + c2 )2
Write in the expanded form: (ab + bc + ca)2
Write in the expanded form: `(x/y + y/z + z/x)^2`
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
Write in the expanded form: `(x + 2y + 4z)^2`
Write in the expand form: `(2x - y + z)^2`
Write in the expanded form: (-2x + 3y + 2z)2
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
Simplify `(a + b + c)^2 + (a - b + c)^2`
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Simplify (2x + p - c)2 - (2x - p + c)2
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.3 [Pages 19 - 20]
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
If a + b = 10 and ab = 21, find the value of a3 + b3
If a − b = 4 and ab = 21, find the value of a3 −b3
If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]
If \[x - \frac{1}{x} = 7\] ,find the value of \[x^3 - \frac{1}{x^3}\]
If \[x - \frac{1}{x} = 5\] ,find the value of \[x^3 - \frac{1}{x^3}\]
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Evaluate of the following:
(103)3
Evaluate of the following:
(98)3
Evaluate of the following:
(9.9)3
Evaluate of the following:
`(10.4)^3`
Evaluate of the following:
(598)3
Evaluate of the following:
(99)3
Evaluate of the following:
1113 − 893
Evaluate of the following:
463+343
Evaluate of the following:
1043 + 963
Evaluate of the following:
933 − 1073
If \[x + \frac{1}{x} = 3\], calculate \[x^2 + \frac{1}{x^2}, x^3 + \frac{1}{x^3}\] and \[x^4 + \frac{1}{x^4}\]
Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
If \[x - \frac{1}{x} = 3 + 2\sqrt{2}\] , find the value of \[x^3 - \frac{1}{x^3}\].
Simplify of the following:
(x+3)3 + (x−3)3
Simplify of the following:
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
Simplify of the following:
(2x − 5y)3 − (2x + 5y)3
If \[x^4 + \frac{1}{x^4} = 194,\] find \[x^3 + \frac{1}{x^3}, x^2 + \frac{1}{x^2}\] and \[x + \frac{1}{x}\]
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.4 [Pages 24 - 25]
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
Find the following product:
(7p4 + q) (49p8 − 7p4q + q2)
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
Find the following product:
Find the following product:
Find the following product:
Find the following product:
Find the following product:
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
(9y2 − 4x2) (81y4 +36x2y2 + 16x4)
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If a + b = 8 and ab = 6, find the value of a3 + b3
If a + b = 6 and ab = 20, find the value of a3 − b3
If x = −2 and y = 1, by using an identity find the value of the following
If x = −2 and y = 1, by using an identity find the value of the following
If x = −2 and y = 1, by using an identity find the value of the following
RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.5 [Pages 28 - 29]
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
Find the following product:
(3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)
Evaluate:
253 − 753 + 503
Evaluate:
483 − 303 − 183
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.6 [Page 29]
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If a + b = 7 and ab = 12, find the value of a2 + b2
If a − b = 5 and ab = 12, find the value of a2 + b2
If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]
If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].
If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]
RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.7 [Pages 30 - 32]
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
25
10
23
27
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
64
14
8
2
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
196
194
192
190
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
927
414
364
322
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
8
10
12
13
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
5
10
15
none of these
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
5
4
3
2
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
35
58
127
none of these
(a − b)3 + (b − c)3 + (c − a)3 =
(a + b + c) (a2 + b2 + c2 − ab − bc − ca)
(a − b) (b − c) (c − a)
3(a − b) ( b− c) (c − a)
none of these
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
1
-1
- \[\frac{1}{2}\]
0
If a − b = −8 and ab = −12, then a3 − b3 =
−244
−240
−224
−260
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
3, x2, − 27x
3, x − 3, x + 3
3, x2, 27x
3, 3, 3
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
10000
6250
7500
3750
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to
x16 − y16
x8 − y8
x8 + y8
x16 + y16
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
27
25
- \[3\sqrt{3}\]
- \[- 3\sqrt{3}\]
If \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]
76
52
64
none of these
If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] =
4
- \[\frac{17}{4}\]
- \[\frac{13}{4}\]
- \[\frac{1}{4}\]
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
25
35
49
30
If a2 + b2 + c2 − ab − bc − ca =0, then
a + b + c
b + c = a
c + a = b
a = b = c
If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]
0
1
-1
3
If a1/3 + b1/3 + c1/3 = 0, then
a + b + c = 0
(a + b + c)3 =27abc
a + b + c = 3abc
a3 + b3 + c3 = 0
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
108
207
669
729
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
3(a + b) ( b+ c) (c + a)
3(a − b) (b − c) (c − a)
(a − b) (b − c) (c − a)
none of these
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
a6 + b6
a6 − b6
a3 − b3
a3 + b3
The product (x2−1) (x4 + x2 + 1) is equal to
x8 − 1
x8 + 1
x6 − 1
x6 + 1
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
- 1
-1
- \[\frac{1}{2}\]
0
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
0
\[\frac{1}{4}\]
- \[\frac{1}{\sqrt{2}}\]
- \[\frac{1}{2}\]
Chapter 4: Algebraic Identities

RD Sharma solutions for Mathematics for Class 9 chapter 4 - Algebraic Identities
RD Sharma solutions for Mathematics for Class 9 chapter 4 (Algebraic Identities) 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 4 Algebraic Identities are Algebraic Identities.
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