# RD Sharma solutions for Mathematics for Class 9 chapter 4 - Algebraic Identities [Latest edition]

## Solutions for Chapter 4: Algebraic Identities

Below listed, you can find solutions for Chapter 4 of CBSE RD Sharma for Mathematics for Class 9.

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4Exercise 4.5Exercise 4.6Exercise 4.7
Exercise 4.1 [Pages 6 - 7]

### RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.1 [Pages 6 - 7]

Exercise 4.1 | Q 1.1 | Page 6

Evaluate the following using identities:

(2x+ 1/x)^2

Exercise 4.1 | Q 1.2 | Page 6

Evaluate the following using identities:

(2x + y) (2x − y)

Exercise 4.1 | Q 1.3 | Page 6

Evaluate the following using identities:

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

Exercise 4.1 | Q 1.4 | Page 6

Evaluate following using identities:

(a - 0.1) (a + 0.1)

Exercise 4.1 | Q 1.5 | Page 6

Evaluate the following using identities:

(1.5x− 0.3y2) (1.5x+ 0.3y2)

Exercise 4.1 | Q 2.1 | Page 7

Evaluate the following using identities:

(399)2

Exercise 4.1 | Q 2.2 | Page 7

Evaluate the following using identities:

(0.98)2

Exercise 4.1 | Q 2.3 | Page 7

Evaluate following using identities:

991 ☓ 1009

Exercise 4.1 | Q 2.4 | Page 7

Evaluate the following using identities:

117 x 83

Exercise 4.1 | Q 3.1 | Page 7

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

Exercise 4.1 | Q 3.2 | Page 7

Simplify the following:

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

Exercise 4.1 | 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

Exercise 4.1 | Q 3.4 | Page 7

Simplify the following

(7.83 + 7.83 - 1.17 xx 1.17)/6.66

Exercise 4.1 | Q 4 | Page 7

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

Exercise 4.1 | Q 5 | Page 7

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

Exercise 4.1 | Q 6 | Page 7

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

Exercise 4.1 | Q 7 | Page 7

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

Exercise 4.1 | Q 8 | Page 7

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

Exercise 4.1 | Q 9 | Page 7

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

Exercise 4.1 | Q 10.1 | Page 7

Simplify the following products:

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

Exercise 4.1 | Q 10.2 | Page 7

Simplify the following products:

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

Exercise 4.1 | Q 11 | Page 7

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

Exercise 4.1 | Q 12 | Page 7

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

Exercise 4.1 | Q 13.1 | Page 7

Simplify the following products:

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

Exercise 4.1 | Q 13.2 | Page 7

Simplify the following products:

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

Exercise 4.1 | Q 13.3 | Page 7

Simplify the following products:

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

Exercise 4.1 | Q 13.4 | Page 7

Simplify the following products:

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

Exercise 4.1 | Q 14 | Page 7

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

Exercise 4.2 [Pages 11 - 12]

### RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.2 [Pages 11 - 12]

Exercise 4.2 | Q 1.01 | Page 11

Write in the expanded form:

(a + 2b + c)^2

Exercise 4.2 | Q 1.02 | Page 11

Write in the expanded form:

(2a - 3b - c)2

Exercise 4.2 | Q 1.03 | Page 11

Write the expanded form:

(-3x + y + z)^2

Exercise 4.2 | Q 1.04 | Page 11

Write in the expanded form:

(m + 2n - 5p)^2

Exercise 4.2 | Q 1.05 | Page 11

Write in the expanded form:

(2 + x - 2y)^2

Exercise 4.2 | Q 1.06 | Page 11

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

Exercise 4.2 | Q 1.07 | Page 11

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

Exercise 4.2 | Q 1.08 | Page 11

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

Exercise 4.2 | Q 1.09 | Page 11

Write in the expanded form:

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

Exercise 4.2 | Q 1.1 | Page 11

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

Exercise 4.2 | Q 1.11 | Page 11

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

Exercise 4.2 | Q 1.12 | Page 11

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

Exercise 4.2 | Q 2 | Page 12

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

Exercise 4.2 | Q 3 | Page 12

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

Exercise 4.2 | Q 4 | Page 12

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

Exercise 4.2 | Q 5 | Page 12

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

Exercise 4.2 | Q 6.1 | Page 12

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

Exercise 4.2 | Q 6.2 | Page 12

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

Exercise 4.2 | Q 6.3 | Page 12

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

Exercise 4.2 | Q 6.4 | Page 12

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

Exercise 4.2 | Q 6.5 | Page 12

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

Exercise 4.2 | 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

Exercise 4.2 | Q 7.2 | Page 12

Simplify the following expressions:

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

Exercise 4.2 | Q 7.3 | Page 12

Simplify the following expressions:

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

Exercise 4.3 [Pages 19 - 20]

### RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.3 [Pages 19 - 20]

Exercise 4.3 | Q 1.1 | Page 19

Find the cube of the following binomials expression :

$\frac{1}{x} + \frac{y}{3}$

Exercise 4.3 | Q 1.2 | Page 19

Find the cube of the following binomials expression :

$\frac{3}{x} - \frac{2}{x^2}$

Exercise 4.3 | Q 1.3 | Page 19

Find the cube of the following binomials expression :

$2x + \frac{3}{x}$

Exercise 4.3 | Q 1.4 | Page 19

Find the cube of the following binomials expression :

$4 - \frac{1}{3x}$

Exercise 4.3 | Q 2 | Page 19

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

Exercise 4.3 | Q 3 | Page 19

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

Exercise 4.3 | Q 4 | Page 20

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

Exercise 4.3 | Q 5 | Page 20

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

Exercise 4.3 | Q 6 | Page 20

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

Exercise 4.3 | Q 7 | Page 20

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

Exercise 4.3 | Q 8 | Page 20

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

Exercise 4.3 | Q 9 | Page 20

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

Exercise 4.3 | Q 10 | Page 20

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

Exercise 4.3 | Q 11.1 | Page 20

Evaluate of the following:

(103)3

Exercise 4.3 | Q 11.2 | Page 20

Evaluate of the following:

(98)3

Exercise 4.3 | Q 11.3 | Page 20

Evaluate of the following:

(9.9)3

Exercise 4.3 | Q 11.4 | Page 20

Evaluate of the following:

(10.4)^3

Exercise 4.3 | Q 11.5 | Page 20

Evaluate of the following:

(598)3

Exercise 4.3 | Q 11.6 | Page 20

Evaluate of the following:

(99)3

Exercise 4.3 | Q 12.1 | Page 20

Evaluate of the following:

1113 − 893

Exercise 4.3 | Q 12.2 | Page 20

Evaluate of the following:

463+343

Exercise 4.3 | Q 12.3 | Page 20

Evaluate of the following:

1043 + 963

Exercise 4.3 | Q 12.4 | Page 20

Evaluate of the following:

933 − 1073

Exercise 4.3 | Q 13 | Page 20

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

Exercise 4.3 | Q 14.1 | Page 20

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

Exercise 4.3 | Q 14.2 | Page 20

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

Exercise 4.3 | Q 15 | Page 20

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

Exercise 4.3 | Q 16 | Page 20

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

Exercise 4.3 | Q 17.1 | Page 20

Simplify of the following:

(x+3)3 + (x−3)3

Exercise 4.3 | Q 17.2 | Page 20

Simplify of the following:

$\left( \frac{x}{2} + \frac{y}{3} \right)^3 - \left( \frac{x}{2} - \frac{y}{3} \right)^3$
Exercise 4.3 | Q 17.3 | Page 20

Simplify of the following:

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

Exercise 4.3 | Q 17.4 | Page 20

Simplify of the following:

(2x − 5y)3 − (2x + 5y)3

Exercise 4.3 | 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 $x + \frac{1}{x}$

Exercise 4.3 | Q 19 | Page 20

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

Exercise 4.4 [Pages 24 - 25]

### RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.4 [Pages 24 - 25]

Exercise 4.4 | Q 1.01 | Page 24

Find the following product:

(3x + 2y) (9x2 − 6xy + 4y2)

Exercise 4.4 | Q 1.02 | Page 24

Find the following product:

(4x − 5y) (16x2 + 20xy + 25y2)

Exercise 4.4 | Q 1.03 | Page 24

Find the following product:

(7p4 + q) (49p8 − 7p4q + q2)

Exercise 4.4 | Q 1.04 | Page 24

Find the following product:

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

Exercise 4.4 | Q 1.05 | Page 24

Find the following product:

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

Exercise 4.4 | Q 1.06 | Page 24

Find the following product:

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

Exercise 4.4 | Q 1.07 | Page 24

Find the following product:

$\left( \frac{2}{x} + 3x \right) \left( \frac{4}{x^2} + 9 x^2 - 6 \right)$
Exercise 4.4 | Q 1.08 | Page 24

Find the following product:

$\left( \frac{3}{x} - 2 x^2 \right) \left( \frac{9}{x^2} + 4 x^4 - 6x \right)$
Exercise 4.4 | Q 1.09 | Page 24

Find the following product:

(1 − x) (1+ x + x2)
Exercise 4.4 | Q 1.1 | Page 24

Find the following product:

(1 + x) (1 − x + x2)
Exercise 4.4 | Q 1.11 | Page 24

Find the following product:

(x2 − 1) (x4 + x2 + 1)
Exercise 4.4 | Q 1.12 | Page 24

Find the following product:

(x3 + 1) (x6 − x3 + 1)
Exercise 4.4 | 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)

Exercise 4.4 | Q 2.2 | Page 24

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

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

Exercise 4.4 | Q 2.3 | Page 24

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

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

Exercise 4.4 | Q 2.4 | Page 24

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

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

Exercise 4.4 | Q 2.5 | Page 24

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

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

Exercise 4.4 | Q 3 | Page 25

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

Exercise 4.4 | Q 4 | Page 25

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

Exercise 4.4 | Q 5 | Page 25

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

Exercise 4.4 | 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)
Exercise 4.4 | Q 6.2 | Page 25

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

$\left( \frac{2}{x} - \frac{x}{2} \right) \left( \frac{4}{x^2} + \frac{x^2}{4} + 1 \right)$
Exercise 4.4 | Q 6.3 | Page 25

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

$\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)$
Exercise 4.5 [Pages 28 - 29]

### RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.5 [Pages 28 - 29]

Exercise 4.5 | Q 1.1 | Page 28

Find the following product:

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

Exercise 4.5 | Q 1.2 | Page 28

Find the following product:

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

Exercise 4.5 | Q 1.3 | Page 28

Find the following product:

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

Exercise 4.5 | Q 1.4 | Page 28

Find the following product:

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

Exercise 4.5 | Q 2.1 | Page 29

Evaluate:

253 − 753 + 503

Exercise 4.5 | Q 2.2 | Page 29

Evaluate:

483 − 303 − 183

Exercise 4.5 | Q 2.3 | Page 29
Evaluate:
$\left( \frac{1}{2} \right)^3 + \left( \frac{1}{3} \right)^3 - \left( \frac{5}{6} \right)^3$
Exercise 4.5 | Q 2.4 | Page 29
Evaluate:
(0.2)3 − (0.3)3 + (0.1)3
Exercise 4.5 | Q 3 | Page 29

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

Exercise 4.5 | Q 4 | Page 29

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

Exercise 4.5 | Q 5 | Page 29

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

Exercise 4.6 [Page 29]

### RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.6 [Page 29]

Exercise 4.6 | Q 1 | Page 29

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

Exercise 4.6 | Q 2 | Page 29

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

Exercise 4.6 | Q 3 | Page 29

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

Exercise 4.6 | Q 4 | Page 29

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

Exercise 4.6 | Q 5 | Page 29

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

Exercise 4.6 | Q 6 | Page 29

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

Exercise 4.6 | Q 7 | Page 29

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

Exercise 4.7 [Pages 30 - 32]

### RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities Exercise 4.7 [Pages 30 - 32]

Exercise 4.7 | 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

Exercise 4.7 | Q 2 | Page 30

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

• 64

• 14

• 8

• 2

Exercise 4.7 | Q 3 | Page 30

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

• 196

• 194

• 192

• 190

Exercise 4.7 | Q 4 | Page 30

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

• 927

• 414

• 364

• 322

Exercise 4.7 | Q 5 | Page 30

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

• 8

• 10

• 12

• 13

Exercise 4.7 | Q 6 | Page 30

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

• 5

• 10

• 15

• none of these

Exercise 4.7 | Q 7 | Page 30

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

• 5

• 4

• 3

• 2

Exercise 4.7 | Q 8 | Page 30

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

• 35

• 58

• 127

•  none of these

Exercise 4.7 | 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

Exercise 4.7 | Q 10 | Page 30

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

• 1

• -1

• $\frac{1}{2}$
• 0

Exercise 4.7 | Q 11 | Page 30

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

• −244

•  −240

• −224

• −260

Exercise 4.7 | 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

Exercise 4.7 | Q 13 | Page 31

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

• 10000

• 6250

• 7500

• 3750

Exercise 4.7 | Q 14 | Page 31

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

• x16 − y16

• x8 − y8

•  x8 + y8

• x16 + y16

Exercise 4.7 | Q 15 | Page 31

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

• 27

• 25

• $3\sqrt{3}$
• $- 3\sqrt{3}$
Exercise 4.7 | 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

Exercise 4.7 | Q 17 | Page 31

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

• 4

• $\frac{17}{4}$
• $\frac{13}{4}$
• $\frac{1}{4}$
Exercise 4.7 | Q 18 | Page 31

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

• 25

• 35

• 49

• 30

Exercise 4.7 | 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

Exercise 4.7 | 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

Exercise 4.7 | 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

Exercise 4.7 | Q 22 | Page 31

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

• 108

• 207

• 669

• 729

Exercise 4.7 | 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

Exercise 4.7 | 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

Exercise 4.7 | Q 25 | Page 32

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

•  x8 − 1

•  x8 + 1

• x6 − 1

• x6   +  1

Exercise 4.7 | Q 26 | Page 32

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

• 1

• -1

• $\frac{1}{2}$
• 0

Exercise 4.7 | 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

• $\frac{1}{4}$

• $\frac{1}{\sqrt{2}}$
• $\frac{1}{2}$

## Solutions for Chapter 4: Algebraic Identities

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4Exercise 4.5Exercise 4.6Exercise 4.7

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

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

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