#### Chapters

Chapter 2: Profit , Loss and Discount

Chapter 3: Compound Interest

Chapter 4: Expansions

Chapter 5: Factorisation

Chapter 6: Changing the subject of a formula

Chapter 7: Linear Equations

Chapter 8: Simultaneous Linear Equations

Chapter 9: Indices

Chapter 10: Logarithms

Chapter 11: Triangles and their congruency

Chapter 12: Isosceles Triangle

Chapter 13: Inequalities in Triangles

Chapter 14: Constructions of Triangles

Chapter 15: Mid-point and Intercept Theorems

Chapter 16: Similarity

Chapter 17: Pythagoras Theorem

Chapter 18: Rectilinear Figures

Chapter 19: Quadrilaterals

Chapter 20: Constructions of Quadrilaterals

Chapter 21: Areas Theorems on Parallelograms

Chapter 22: Statistics

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Perimeter and Area

Chapter 25: Surface Areas and Volume of Solids

Chapter 26: Trigonometrical Ratios

Chapter 27: Trigonometrical Ratios of Standard Angles

Chapter 28: Coordinate Geometry

## Chapter 4: Expansions

### Frank solutions for Class 9 Maths ICSE Chapter 4 Expansions Exercise 4.1

Expand the following:

(a + 4) (a + 7)

Expand the following:

(m + 8) (m - 7)

Expand the following:

(x - 5) (x - 4)

Expand the following:

(3x + 4) (2x - 1)

Expand the following:

(2x - 5) (2x + 5) (2x- 3)

Expand the following:

(a + 3b)^{2}

Expand the following:

(2p - 3q)^{2}

Expand the following:

`(2"a" + 1/(2"a"))^2`

Expand the following:

(x - 3y - 2z)^{2}

Find the squares of the following:

9m - 2n

Find the squares of the following:

3p - 4q^{2}

Find the squares of the following:

`(7x)/(9y) - (9y)/(7x)`

Find the squares of the following:

(2a + 3b - 4c)

Simplify by using formula :

(5x - 9) (5x + 9)

Simplify by using formula :

(2x + 3y) (2x - 3y)

Simplify by using formula :

(a + b - c) (a - b + c)

Simplify by using formula :

(x + y - 3) (x + y + 3)

Simplify by using formula :

(1 + a) (1 - a) (1 + a^{2})

Simplify by using formula :

`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`

Evaluate the following without multiplying:

(95)^{2}

Evaluate the following without multiplying:

(103)^{2}

Evaluate the following without multiplying:

(999)^{2}

Evaluate the following without multiplying:

(1005)^{2}

Evaluate, using (a + b)(a - b)= a^{2} - b^{2}.

399 x 401

Evaluate, using (a + b)(a - b)= a^{2} - b^{2}.

999 x 1001

Evaluate, using (a + b)(a - b)= a^{2} - b^{2}.

4.9 x 5.1

Evaluate, using (a + b)(a - b)= a^{2} - b^{2}.

15.9 x 16.1

If a - b = 10 and ab = 11; find a + b.

If x + y = 9, xy = 20

find: x - y

If x + y = 9, xy = 20

find: x^{2} - y^{2}.

If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`

If `"a" + 1/"a" = 6;`find `"a"^2 - 1/"a"^2`

If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`

If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`

If `x + (1)/x = 3`; find `x^2 + (1)/x^2`

If `x + (1)/x = 3`; find `x^4 + (1)/x^4`

If p + q = 8 and p - q = 4, find:

pq

If p + q = 8 and p - q = 4, find:

p^{2 }+ q^{2}

If m - n = 0.9 and mn = 0.36, find:

m + n

If m - n = 0.9 and mn = 0.36, find:

m^{2} - n^{2}.

If x + y = 1 and xy = -12; find:

x - y

If x + y = 1 and xy = -12; find:

x^{2} - y^{2}.

If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :

`"a" + (1)/"a"`

If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :

`"a"^2 + (1)/"a"^2`

If a^{2} - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`

If a^{2} - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`

If a^{2} - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`

If 2x + 3y = 10 and xy = 5; find the value of 4x^{2} + 9y^{2}

If x + y + z = 12 and xy + yz + zx = 27; find x^{2} + y^{2} + z^{2}.

If a^{2} + b^{2} + c^{2} = 41 and a + b + c = 9; find ab + bc + ca.

If p^{2} + q^{2} + r^{2} = 82 and pq + qr + pr = 18; find p + q + r.

If x + y + z = p and xy + yz + zx = q; find x^{2} + y^{2} + z^{2}.

### Frank solutions for Class 9 Maths ICSE Chapter 4 Expansions Exercise 4.2

Find the cube of: 2a - 5b

Find the cube of: 4x + 7y

Find the cube of: `3"a" + (1)/(3"a")`

Find the cube of: `4"p" - (1)/"p"`

Find the cube of: `(2"m")/(3"n") + (3"n")/(2"m")`

Find the cube of: `"a" - (1)/"a" + "b"`

If `5x + (1)/(5x) = 7`; find the value of `125x^3 + (1)/(125x^3)`.

If `3x - (1)/(3x) = 9`; find the value of `27x^3 - (1)/(27x^3)`.

If `x + (1)/x = 5`, find the value of `x^2 + (1)/x^2, x^3 + (1)/x^3` and `x^4 + (1)/x^4`.

If `"a" - (1)/"a" = 7`, find `"a"^2 + (1)/"a"^2 , "a"^2 - (1)/"a"^2` and `"a"^3 - (1)/"a"^3`

If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`

If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a"^3 + (1)/"a"^3`

If `"m"^2 + (1)/"m"^2 = 51`; find the value of `"m"^3 - (1)/"m"^3`

If `9"a"^2 + (1)/(9"a"^2) = 23`; find the value of `27"a"^3 + (1)/(27"a"^3)`

If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`

If `x^2 + (1)/x^2 = 18`; find : `x^3 - (1)/x^3`

If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`

If `"p" + (1)/"p" = 6`; find : `"p"^4 + (1)/"p"^4`

If `"p" + (1)/"p" = 6`; find : `"p"^3 + (1)/"p"^3`

If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`

If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`

If `"r" - (1)/"r" = 4`; find : `"r"^3 - (1)/"r"^3`

If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`

If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.

If `"a" + (1)/"a" = "p"`; then show that `"a"^3 + (1)/"a"^3 = "p"("p"^2 - 3)`

If `("a" + 1/"a")^2 = 3`; then show that `"a"^3 + (1)/"a"^3 = 0`

If a + b + c = 0; then show that a^{3} + b^{3} + c^{3} = 3abc.

If a + 2b + c = 0; then show that a^{3} + 8b^{3} + c^{3} = 6abc

If x^{3} + y^{3} = 9 and x + y = 3, find xy.

If a + b = 5 and ab = 2, find a^{3 }+ b^{3}.

If p - q = -1 and pq = -12, find p^{3} - q^{3}

If m - n = -2 and m^{3} - n^{3} = -26, find mn.

If 2a - 3b = 10 and ab = 16; find the value of 8a^{3} - 27b^{3}.

If x + 2y = 5, then show that x^{3} + 8y^{3} + 30xy = 125.

Simplify:

(4x + 5y)^{2} + (4x - 5y)^{2}

Simplify:

(7a +5b)^{2} - (7a - 5b)^{2}

Simplify:

(a + b)^{3} + (a - b)^{3}

Simplify:

`("a" - 1/"a")^2 + ("a" + 1/"a")^2`

Simplify:

(x + y - z)^{2} + (x - y + z)^{2}

Simplify:

`("a" + 1/"a")^3 - ("a" - 1/"a")^3`

Simplify:

(2x + y)(4x^{2} - 2xy + y^{2})

Simplify:

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

Simplify:

(x + 2y + 3z)(x^{2} + 4y^{2} + 9z^{2} - 2xy - 6yz - 3zx)

Simplify:

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

Simplify:

(3a + 2b - c)(9a^{2} + 4b^{2} + c^{2} - 6ab + 2bc +3ca)

Simplify:

(3x + 5y + 2z)(3x - 5y + 2z)

Simplify:

(2x - 4y + 7)(2x + 4y + 7)

Simplify:

(3a - 7b + 3)(3a - 7b + 5)

Evaluate the following :

(3.29)^{3} + (6.71)^{3}

Evaluate the following :

(5.45)^{3} + (3.55)^{3}

Evaluate the following :

(8.12)^{3} - (3.12)^{3}

Evaluate the following :

7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16

Evaluate the following :

1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19

## Chapter 4: Expansions

## Frank solutions for Class 9 Maths ICSE chapter 4 - Expansions

Frank solutions for Class 9 Maths ICSE chapter 4 (Expansions) 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 CISCE Class 9 Maths ICSE 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. Frank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Maths ICSE chapter 4 Expansions are Algebraic Identities, Expansion of Formula, Special Product, Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method, Expansion of (a + b)3.

Using Frank Class 9 solutions Expansions 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 Frank Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 9 prefer Frank Textbook Solutions to score more in exam.

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