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

## Chapter 4: Algebraic Identities

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4Exercise 4.5Others
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 4.5 [Page 29]

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

Exercise 4.5 | Q 1 | Page 29

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

Exercise 4.5 | Q 2 | Page 29

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

Exercise 4.5 | Q 3 | Page 29

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

Exercise 4.5 | Q 4 | Page 29

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

Exercise 4.5 | 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 4.5 | Q 6 | Page 29

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

Exercise 4.5 | Q 7 | Page 29

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

[Pages 30 - 32]

### RD Sharma solutions for Mathematics for Class 9 Chapter 4 Algebraic Identities [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

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4Exercise 4.5Others

## 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.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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

Using RD Sharma Class 9 solutions Algebraic Identities exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer RD Sharma Textbook Solutions to score more in exam.

Get the free view of chapter 4 Algebraic Identities Class 9 extra questions for Mathematics for Class 9 and can use Shaalaa.com to keep it handy for your exam preparation