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RD Sharma solutions for Class 9 Mathematics chapter 4 - Algebraic Identities

Mathematics for Class 9 by R D Sharma (2018-19 Session)

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RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

Mathematics for Class 9 by R D Sharma (2018-19 Session)

Chapter 4: Algebraic Identities

Ex. 4.10Ex. 4.20Ex. 4.30Ex. 4.40Ex. 4.50Others

Chapter 4: Algebraic Identities Exercise 4.10 solutions [Pages 6 - 7]

Ex. 4.10 | Q 1.1 | Page 6

Evaluate the following using identities:

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

Ex. 4.10 | Q 1.2 | Page 6

Evaluate the following using identities:

(2x + y) (2x − y)

Ex. 4.10 | Q 1.3 | Page 6

Evaluate the following using identities:

`(a^2b - b^2a)^2`

Ex. 4.10 | Q 1.4 | Page 6

Evaluate following using identities:

(a - 0.1) (a + 0.1)

Ex. 4.10 | Q 1.5 | Page 6

Evaluate the following using identities:

(1.5x− 0.3y2) (1.5x+ 0.3y2)

Ex. 4.10 | Q 2.1 | Page 7

Evaluate the following using identities:

(399)2

Ex. 4.10 | Q 2.2 | Page 7

Evaluate the following using identities:

(0.98)2

Ex. 4.10 | Q 2.3 | Page 7

Evaluate following using identities:

991 ☓ 1009

Ex. 4.10 | Q 2.4 | Page 7

Evaluate the following using identities:

117 x 83

Ex. 4.10 | Q 3.1 | Page 7

Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25

Ex. 4.10 | Q 3.2 | Page 7

Simplify the following:

322 x 322 - 2 x 322 x 22 + 22 x 22

Ex. 4.10 | Q 3.3 | Page 7

Simplify the following:

0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24

Ex. 4.10 | Q 3.4 | Page 7

Simplify the following

`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`

Ex. 4.10 | Q 4 | Page 7

if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`

Ex. 4.10 | Q 5 | Page 7

If \[x - \frac{1}{x} = - 1\]  find the value of  \[x^2 + \frac{1}{x^2}\]

Ex. 4.10 | Q 6 | Page 7

If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`

Ex. 4.10 | Q 7 | Page 7

If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y

Ex. 4.10 | Q 8 | Page 7

If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`

Ex. 4.10 | Q 9 | Page 7

If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`

Ex. 4.10 | Q 10.1 | Page 7

Simplify the following products:

`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`

Ex. 4.10 | Q 10.2 | Page 7

Simplify the following products:

`(m + n/7)^3 (m - n/7)`

Ex. 4.10 | Q 11 | Page 7

If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`

Ex. 4.10 | Q 12 | Page 7

if `x^2 + 1/x^2 = 79` Find the value of `x + 1/x`

Ex. 4.10 | Q 13.1 | Page 7

Simplify the following products:

`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`

Ex. 4.10 | Q 13.2 | Page 7

Simplify the following products:

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

Ex. 4.10 | Q 13.3 | Page 7

Simplify the following products:

`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`

Ex. 4.10 | Q 13.4 | Page 7

Simplify the following products:

`(2x^4 - 4x^2 + 1)(2x^4 - 4x^2 - 1)`

Ex. 4.10 | Q 14 | Page 7

Prove that a2 + b2 + c2 − ab − bc − ca is always non-negative for all values of a, b and c

Chapter 4: Algebraic Identities Exercise 4.20 solutions [Pages 11 - 12]

Ex. 4.20 | Q 1.01 | Page 11

Write in the expanded form:

`(a + 2b + c)^2`

Ex. 4.20 | Q 1.02 | Page 11

Write in the expanded form:

(2a - 3b - c)2

Ex. 4.20 | Q 1.03 | Page 11

Write the expanded form:

`(-3x + y + z)^2`

Ex. 4.20 | Q 1.04 | Page 11

Write in the expanded form:

`(m + 2n - 5p)^2`

Ex. 4.20 | Q 1.05 | Page 11

Write in the expanded form:

`(2 + x - 2y)^2`

Ex. 4.20 | Q 1.06 | Page 11

Write in the expanded form (a2 + b2 + c2 )2

Ex. 4.20 | Q 1.07 | Page 11

Write in the expanded form: (ab + bc + ca)2

 

Ex. 4.20 | Q 1.08 | Page 11

Write in the expanded form: `(x/y + y/z + z/x)^2`

Ex. 4.20 | Q 1.09 | Page 11

Write in the expanded form:

`(a/(bc) + b/(ca) + c/(ab))^2`

Ex. 4.20 | Q 1.1 | Page 11

Write in the expanded form: `(x + 2y + 4z)^2`

Ex. 4.20 | Q 1.11 | Page 11

Write in the expand form: `(2x - y + z)^2`

Ex. 4.20 | Q 1.12 | Page 11

Write in the expanded form: (-2x + 3y + 2z)2

Ex. 4.20 | Q 2 | Page 12

If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.

Ex. 4.20 | Q 3 | Page 12

If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.

Ex. 4.20 | Q 4 | Page 12

If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.

Ex. 4.20 | Q 5 | Page 12

Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.

Ex. 4.20 | Q 6.1 | Page 12

Simplify `(a + b + c)^2 + (a - b + c)^2`

Ex. 4.20 | Q 6.2 | Page 12

Simplify: `(a + b + c)^2 - (a - b + c)^2` 

Ex. 4.20 | Q 6.3 | Page 12

Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2

Ex. 4.20 | Q 6.4 | Page 12

Simplify (2x + p - c)2 - (2x - p + c)2

Ex. 4.20 | Q 6.5 | Page 12

Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`

Ex. 4.20 | Q 7.1 | Page 12

Simplify the expression: 

`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`

Ex. 4.20 | Q 7.2 | Page 12

Simplify the following expressions:

`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`

Ex. 4.20 | Q 7.3 | Page 12

Simplify the following expressions:

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

Chapter 4: Algebraic Identities Exercise 4.30 solutions [Pages 19 - 20]

Ex. 4.30 | Q 1.1 | Page 19

Find the cube of the following binomials expression :

\[\frac{1}{x} + \frac{y}{3}\]

Ex. 4.30 | Q 1.2 | Page 19

Find the cube of the following binomials expression :

\[\frac{3}{x} - \frac{2}{x^2}\]

Ex. 4.30 | Q 1.3 | Page 19

Find the cube of the following binomials expression :

\[2x + \frac{3}{x}\]

Ex. 4.30 | Q 1.4 | Page 19

Find the cube of the following binomials expression :

\[4 - \frac{1}{3x}\]

Ex. 4.30 | Q 2 | Page 19

If a + b = 10 and ab = 21, find the value of a3 + b3

Ex. 4.30 | Q 3 | Page 19

If a − b = 4 and ab = 21, find the value of a3 −b3

Ex. 4.30 | Q 4 | Page 20

If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]

Ex. 4.30 | Q 5 | Page 20

If \[x - \frac{1}{x} = 7\] ,find the value of \[x^3 - \frac{1}{x^3}\]

Ex. 4.30 | Q 6 | Page 20

If  \[x - \frac{1}{x} = 5\] ,find the value of \[x^3 - \frac{1}{x^3}\]

Ex. 4.30 | Q 7 | Page 20

If  \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]

Ex. 4.30 | Q 8 | Page 20

If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]

Ex. 4.30 | Q 9 | Page 20

If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3

Ex. 4.30 | Q 10 | Page 20

If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3

Ex. 4.30 | Q 11.1 | Page 20

Evaluate of the following:

(103)3

Ex. 4.30 | Q 11.2 | Page 20

Evaluate of the following:

 (98)3

Ex. 4.30 | Q 11.3 | Page 20

Evaluate of the following:

 (9.9)3

Ex. 4.30 | Q 11.4 | Page 20

Evaluate of the following: 

`(10.4)^3`

Ex. 4.30 | Q 11.5 | Page 20

Evaluate of the following: 

 (598)3

Ex. 4.30 | Q 11.6 | Page 20

Evaluate of the following: 

(99)3

Ex. 4.30 | Q 12.1 | Page 20

Evaluate of the following:

 1113 − 893

Ex. 4.30 | Q 12.2 | Page 20

Evaluate of the following:

 463+343

Ex. 4.30 | Q 12.3 | Page 20

Evaluate of the following:

1043 + 963

Ex. 4.30 | Q 12.4 | Page 20

Evaluate of the following:

933 − 1073

Ex. 4.30 | Q 13 | Page 20

If \[x + \frac{1}{x} = 3\], calculate  \[x^2 + \frac{1}{x^2}, x^3 + \frac{1}{x^3}\] and \[x^4 + \frac{1}{x^4}\]

Ex. 4.30 | Q 14.1 | Page 20

Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8

Ex. 4.30 | Q 14.2 | Page 20

Find the value of 27x3 + 8y3, if  3x + 2y = 20 and xy = \[\frac{14}{9}\]

Ex. 4.30 | Q 15 | Page 20

Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.

Ex. 4.30 | Q 16 | Page 20

If \[x - \frac{1}{x} = 3 + 2\sqrt{2}\] , find the value of \[x^3 - \frac{1}{x^3}\].

Ex. 4.30 | Q 17.1 | Page 20

Simplify of the following:

(x+3)3 + (x−3)3

Ex. 4.30 | Q 17.2 | Page 20

Simplify of the following:

\[\left( \frac{x}{2} + \frac{y}{3} \right)^3 - \left( \frac{x}{2} - \frac{y}{3} \right)^3\]
Ex. 4.30 | Q 17.3 | Page 20

Simplify of the following:

\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]

Ex. 4.30 | Q 17.4 | Page 20

Simplify of the following:

(2x − 5y)3 − (2x + 5y)3

Ex. 4.30 | Q 18 | Page 20

If \[x^4 + \frac{1}{x^4} = 194,\] find \[x^3 + \frac{1}{x^3}, x^2 + \frac{1}{x^2}\] and \[x + \frac{1}{x}\]

Ex. 4.30 | Q 19 | Page 20

If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]

Chapter 4: Algebraic Identities Exercise 4.40 solutions [Pages 24 - 25]

Ex. 4.40 | Q 1.01 | Page 24

Find the following product:

(3x + 2y) (9x2 − 6xy + 4y2)

Ex. 4.40 | Q 1.02 | Page 24

Find the following product:

(4x − 5y) (16x2 + 20xy + 25y2)

Ex. 4.40 | Q 1.03 | Page 24

Find the following product:

 (7p4 + q) (49p8 − 7p4q + q2)

Ex. 4.40 | Q 1.04 | Page 24

Find the following product:

\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]

Ex. 4.40 | Q 1.05 | Page 24

Find the following product:

\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]

Ex. 4.40 | Q 1.06 | Page 24

Find the following product:

\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]

Ex. 4.40 | Q 1.07 | Page 24

Find the following product:

\[\left( \frac{2}{x} + 3x \right) \left( \frac{4}{x^2} + 9 x^2 - 6 \right)\]
Ex. 4.40 | Q 1.08 | Page 24

Find the following product:

\[\left( \frac{3}{x} - 2 x^2 \right) \left( \frac{9}{x^2} + 4 x^4 - 6x \right)\]
Ex. 4.40 | Q 1.09 | Page 24

Find the following product:

(1 − x) (1+ x + x2)
Ex. 4.40 | Q 1.1 | Page 24

Find the following product:

(1 + x) (1 − x + x2)
Ex. 4.40 | Q 1.11 | Page 24

Find the following product:

(x2 − 1) (x4 + x2 + 1)
Ex. 4.40 | Q 1.12 | Page 24

Find the following product:

(x3 + 1) (x6 − x3 + 1)
Ex. 4.40 | Q 2.1 | Page 24

If x = 3 and y = − 1, find the values of the following using in identify:

 (9y− 4x2) (81y4 +36x2y2 + 16x4)

Ex. 4.40 | Q 2.2 | Page 24

If x = 3 and y = − 1, find the values of the following using in identify:

\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]

Ex. 4.40 | Q 2.3 | Page 24

If x = 3 and y = − 1, find the values of the following using in identify:

\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]

Ex. 4.40 | Q 2.4 | Page 24

If x = 3 and y = − 1, find the values of the following using in identify:

\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]

Ex. 4.40 | Q 2.5 | Page 24

If x = 3 and y = − 1, find the values of the following using in identify:

\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]

Ex. 4.40 | Q 3 | Page 25

If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2

Ex. 4.40 | Q 4 | Page 25

If a + b = 8 and ab = 6, find the value of a3 + b3

Ex. 4.40 | Q 5 | Page 25

If a + b = 6 and ab = 20, find the value of a3 − b3

Ex. 4.40 | Q 6.1 | Page 25

If x = −2 and y = 1, by using an identity find the value of the following

 4y2 − 9x2 (16y4 + 36x2y2+81x4)
Ex. 4.40 | Q 6.2 | Page 25

If x = −2 and y = 1, by using an identity find the value of the following

\[\left( \frac{2}{x} - \frac{x}{2} \right) \left( \frac{4}{x^2} + \frac{x^2}{4} + 1 \right)\]
Ex. 4.40 | Q 6.3 | Page 25

If x = −2 and y = 1, by using an identity find the value of the following

\[\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)\]

Chapter 4: Algebraic Identities Exercise 4.50 solutions [Pages 28 - 29]

Ex. 4.50 | Q 1.1 | Page 28

Find the following product:

(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)

Ex. 4.50 | Q 1.2 | Page 28

Find the following product:

(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)

Ex. 4.50 | Q 1.3 | Page 28

Find the following product:

(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)

Ex. 4.50 | Q 1.4 | Page 28

Find the following product:

(3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)

Ex. 4.50 | Q 2.1 | Page 29

Evaluate:

253 − 753 + 503

Ex. 4.50 | Q 2.2 | Page 29

Evaluate:

483 − 303 − 183

Ex. 4.50 | Q 2.3 | Page 29
Evaluate:
\[\left( \frac{1}{2} \right)^3 + \left( \frac{1}{3} \right)^3 - \left( \frac{5}{6} \right)^3\]
Ex. 4.50 | Q 2.4 | Page 29
Evaluate:
(0.2)3 − (0.3)3 + (0.1)3
Ex. 4.50 | Q 3 | Page 29

If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz

Ex. 4.50 | Q 4 | Page 29

If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc

Ex. 4.50 | Q 5 | Page 29

If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b+ c3 −3abc

Chapter 4: Algebraic Identities Exercise 4.50 solutions [Page 29]

Ex. 4.50 | Q 1 | Page 29

If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].

Ex. 4.50 | Q 2 | Page 29

If \[x + \frac{1}{x} = 3\]  then find the value of \[x^6 + \frac{1}{x^6}\].

Ex. 4.50 | Q 3 | Page 29

If a + b = 7 and ab = 12, find the value of a2 + b2

Ex. 4.50 | Q 4 | Page 29

If a − b = 5 and ab = 12, find the value of a2 + b2

Ex. 4.50 | Q 5 | Page 29

If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]

Ex. 4.50 | Q 6 | Page 29

If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].

Ex. 4.50 | Q 7 | Page 29

If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]

Chapter 4: Algebraic Identities solutions [Pages 30 - 32]

Q 1 | Page 30

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

Q 2 | Page 30

If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]

  • 64

  • 14

  • 8

  • 2

Q 3 | Page 30

If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]

  • 196

  • 194

  • 192

  • 190

Q 4 | Page 30

If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] = 

 

  • 927

  • 414

  • 364

  • 322

Q 5 | Page 30

If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] = 

  • 8

  • 10

  • 12

  • 13

Q 6 | Page 30

If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]

  • 5

  • 10

  • 15

  • none of these

Q 7 | Page 30

If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]

 

  • 5

  • 4

  • 3

  • 2

Q 8 | Page 30

If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =

  • 35

  • 58

  • 127

  •  none of these

Q 9 | Page 30

(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

Q 10 | Page 30

If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =

 

  • 1

  • -1

  • \[\frac{1}{2}\]
  • 0

Q 11 | Page 30

If a − b = −8 and ab  = −12, then a3 − b3 =

  • −244

  •  −240

  • −224

  • −260

Q 12 | Page 31

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

Q 13 | Page 31

75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to

  • 10000

  • 6250

  • 7500

  • 3750

Q 14 | Page 31

(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to

  • x16 − y16

  • x8 − y8

  •  x8 + y8

  • x16 + y16

Q 15 | Page 31

If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]

  • 27

  • 25

  • \[3\sqrt{3}\]
  • \[- 3\sqrt{3}\]
Q 16 | Page 31

If  \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]

  • 76

  • 52

  • 64

  • none of these

Q 17 | Page 31

If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] = 

  • 4

  • \[\frac{17}{4}\]
  • \[\frac{13}{4}\]
  • \[\frac{1}{4}\]
Q 18 | Page 31

If  \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]

  • 25

  • 35

  • 49

  • 30

Q 19 | Page 31

If a2 + b2 + c2 − ab − bc − ca =0, then

  • a + b + c

  •  b + c = a

  •  c + a = b

  • a = b = c

Q 20 | Page 31

If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]

  • 0

  • 1

  • -1

  • 3

Q 21 | Page 31

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

Q 22 | Page 31

If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =

  • 108

  • 207

  • 669

  • 729

Q 23 | Page 31

\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]

  • 3(a + b) ( b+ c) (c + a)

  • 3(a − b) (b − c) (c − a)

  • (a − b) (b − c) (c − a)

  • none of these

Q 24 | Page 32

The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to

  • a6 + b6

  • a6 − b6

  •  a3 − b3

  • a3 + b3

Q 25 | Page 32

The product (x2−1) (x4 + x2 + 1) is equal to

  •  x8 − 1

  •  x8 + 1

  • x6 − 1

  • x6   +  1

Q 26 | Page 32

If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =

  • 1

     

  • -1

  • \[\frac{1}{2}\]
  • 0

Q 27 | Page 32

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

Ex. 4.10Ex. 4.20Ex. 4.30Ex. 4.40Ex. 4.50Others

RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

Mathematics for Class 9 by R D Sharma (2018-19 Session)

RD Sharma solutions for Class 9 Mathematics chapter 4 - Algebraic Identities

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Concepts covered in Class 9 Mathematics chapter 4 Algebraic Identities are Algebraic Identities.

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