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# R.D. Sharma solutions Mathematics for Class 9 by R D Sharma (2018-19 Session) chapter 4 Algebraic Identities

## Chapter 4 - Algebraic Identities

#### Pages 0 - 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:

(1.5x− 0.3y2) (1.5x+ 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

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

Simplify the following

(7.83 + 7.83 - 1.17 xx 1.17)/6.66

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

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

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

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)

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^2 - 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

#### Page 0

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

Evaluate the following using identities:

(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

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

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 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

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