#### 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 - Introduction to Euclid’s Geometry

Chapter 8 - Lines and Angles

Chapter 9 - Triangle and its Angles

Chapter 10 - Congruent Triangles

Chapter 11 - Co-ordinate Geometry

Chapter 12 - Heron’s Formula

Chapter 13 - Linear Equations in Two Variables

Chapter 14 - Quadrilaterals

Chapter 15 - Areas of Parallelograms and Triangles

Chapter 16 - Circles

Chapter 17 - Constructions

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

#### 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^{2 }− 0.3y^{2}) (1.5x^{2 }+ 0.3y^{2})

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 9x^{2} + 25y^{2} = 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 a^{2} + b^{2} + c^{2} − 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 (a^{2} + b^{2} + c^{2} )^{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 a^{2} + b^{2} + c^{2} = 16, find the value of ab + bc + ca.

If a^{2} + b^{2} + c^{2} = 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 a^{2} + b^{2} + c^{2}.

Find the value of 4x^{2} + y^{2} + 25z^{2} + 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`