# Frank solutions for Class 9 Maths ICSE chapter 4 - Expansions [Latest edition]

## Chapter 4: Expansions

Exercise 4.1Exercise 4.2
Exercise 4.1

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

Exercise 4.1 | Q 1.1

Expand the following:
(a + 4) (a + 7)

Exercise 4.1 | Q 1.2

Expand the following:
(m + 8) (m - 7)

Exercise 4.1 | Q 1.3

Expand the following:
(x - 5) (x - 4)

Exercise 4.1 | Q 1.4

Expand the following:
(3x + 4) (2x - 1)

Exercise 4.1 | Q 1.5

Expand the following:
(2x - 5) (2x + 5) (2x- 3)

Exercise 4.1 | Q 2.1

Expand the following:
(a + 3b)2

Exercise 4.1 | Q 2.2

Expand the following:
(2p - 3q)2

Exercise 4.1 | Q 2.3

Expand the following:

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

Exercise 4.1 | Q 2.4

Expand the following:
(x - 3y - 2z)2

Exercise 4.1 | Q 3.1

Find the squares of the following:
9m - 2n

Exercise 4.1 | Q 3.2

Find the squares of the following:
3p - 4q2

Exercise 4.1 | Q 3.3

Find the squares of the following:

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

Exercise 4.1 | Q 3.4

Find the squares of the following:
(2a + 3b - 4c)

Exercise 4.1 | Q 4.1

Simplify by using formula :
(5x - 9) (5x + 9)

Exercise 4.1 | Q 4.2

Simplify by using formula :
(2x + 3y) (2x - 3y)

Exercise 4.1 | Q 4.3

Simplify by using formula :
(a + b - c) (a - b + c)

Exercise 4.1 | Q 4.4

Simplify by using formula :
(x + y - 3) (x + y + 3)

Exercise 4.1 | Q 4.5

Simplify by using formula :
(1 + a) (1 - a) (1 + a2)

Exercise 4.1 | Q 4.6

Simplify by using formula :

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

Exercise 4.1 | Q 5.1

Evaluate the following without multiplying:
(95)2

Exercise 4.1 | Q 5.2

Evaluate the following without multiplying:
(103)2

Exercise 4.1 | Q 5.3

Evaluate the following without multiplying:
(999)2

Exercise 4.1 | Q 5.4

Evaluate the following without multiplying:
(1005)2

Exercise 4.1 | Q 6.1

Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401

Exercise 4.1 | Q 6.2

Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001

Exercise 4.1 | Q 6.3

Evaluate, using (a + b)(a - b)= a2 - b2.
4.9 x 5.1

Exercise 4.1 | Q 6.4

Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1

Exercise 4.1 | Q 7

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

Exercise 4.1 | Q 8.1

If x + y = 9, xy = 20
find: x - y

Exercise 4.1 | Q 8.2

If x + y = 9, xy = 20
find: x2 - y2.

Exercise 4.1 | Q 9.1

If "a"  + 1/"a" = 6;find "a"  - 1/"a"

Exercise 4.1 | Q 9.2

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

Exercise 4.1 | Q 10.1

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

Exercise 4.1 | Q 10.2

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

Exercise 4.1 | Q 11.1

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

Exercise 4.1 | Q 11.2

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

Exercise 4.1 | Q 12.1

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

Exercise 4.1 | Q 12.2

If p + q = 8 and p - q = 4, find:
p2 + q2

Exercise 4.1 | Q 13.1

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

Exercise 4.1 | Q 13.2

If m - n = 0.9 and mn = 0.36, find:
m2 - n2.

Exercise 4.1 | Q 14.1

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

Exercise 4.1 | Q 14.2

If x + y = 1 and xy = -12; find:
x2 - y2.

Exercise 4.1 | Q 15.1

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

"a"  + (1)/"a"

Exercise 4.1 | Q 15.2

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

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

Exercise 4.1 | Q 16.1

If a2 - 3a - 1 = 0 and a ≠ 0, find : "a"  - (1)/"a"

Exercise 4.1 | Q 16.2

If a2 - 3a - 1 = 0 and a ≠ 0, find : "a"  + (1)/"a"

Exercise 4.1 | Q 16.3

If a2 - 3a - 1 = 0 and a ≠ 0, find : "a"^2 - (1)/"a"^2

Exercise 4.1 | Q 17

If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2

Exercise 4.1 | Q 18

If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.

Exercise 4.1 | Q 19

If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.

Exercise 4.1 | Q 20

If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.

Exercise 4.1 | Q 21

If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.

Exercise 4.2

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

Exercise 4.2 | Q 1.1

Find the cube of: 2a - 5b

Exercise 4.2 | Q 1.2

Find the cube of: 4x + 7y

Exercise 4.2 | Q 1.3

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

Exercise 4.2 | Q 1.4

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

Exercise 4.2 | Q 1.5

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

Exercise 4.2 | Q 1.6

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

Exercise 4.2 | Q 2

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

Exercise 4.2 | Q 3

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

Exercise 4.2 | Q 4

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.

Exercise 4.2 | Q 5

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

Exercise 4.2 | Q 6.1

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

Exercise 4.2 | Q 6.2

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

Exercise 4.2 | Q 7

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

Exercise 4.2 | Q 8

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

Exercise 4.2 | Q 9.1

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

Exercise 4.2 | Q 9.2

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

Exercise 4.2 | Q 10.1

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

Exercise 4.2 | Q 10.2

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

Exercise 4.2 | Q 10.3

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

Exercise 4.2 | Q 11.1

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

Exercise 4.2 | Q 11.2

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

Exercise 4.2 | Q 11.3

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

Exercise 4.2 | Q 12

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

Exercise 4.2 | Q 13

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

Exercise 4.2 | Q 14

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

Exercise 4.2 | Q 15

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

Exercise 4.2 | Q 16

If a + b + c = 0; then show that a3 + b3 + c3 = 3abc.

Exercise 4.2 | Q 17

If a + 2b + c = 0; then show that a3 + 8b3 + c3 = 6abc

Exercise 4.2 | Q 18

If x3 + y3 = 9 and x + y = 3, find xy.

Exercise 4.2 | Q 19

If a + b = 5 and ab = 2, find a+ b3.

Exercise 4.2 | Q 20

If p - q = -1 and pq = -12, find p3 - q3

Exercise 4.2 | Q 21

If m - n = -2 and m3 - n3 = -26, find mn.

Exercise 4.2 | Q 22

If 2a - 3b = 10 and ab = 16; find the value of 8a3 - 27b3.

Exercise 4.2 | Q 23

If x + 2y = 5, then show that x3 + 8y3 + 30xy = 125.

Exercise 4.2 | Q 24.01

Simplify:
(4x + 5y)2 + (4x - 5y)2

Exercise 4.2 | Q 24.02

Simplify:
(7a +5b)2 - (7a - 5b)2

Exercise 4.2 | Q 24.03

Simplify:
(a + b)3 + (a - b)3

Exercise 4.2 | Q 24.04

Simplify:

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

Exercise 4.2 | Q 24.05

Simplify:
(x + y - z)2 + (x - y + z)2

Exercise 4.2 | Q 24.06

Simplify:

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

Exercise 4.2 | Q 24.07

Simplify:
(2x + y)(4x2 - 2xy + y2)

Exercise 4.2 | Q 24.08

Simplify:

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

Exercise 4.2 | Q 24.09

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

Exercise 4.2 | Q 24.1

Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)

Exercise 4.2 | Q 24.11

Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)

Exercise 4.2 | Q 24.12

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

Exercise 4.2 | Q 24.13

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

Exercise 4.2 | Q 24.14

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

Exercise 4.2 | Q 25.1

Evaluate the following :
(3.29)3 + (6.71)3

Exercise 4.2 | Q 25.2

Evaluate the following :
(5.45)3 + (3.55)3

Exercise 4.2 | Q 25.3

Evaluate the following :
(8.12)3 - (3.12)3

Exercise 4.2 | Q 25.4

Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16

Exercise 4.2 | Q 25.5

Evaluate the following :
1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19

## Chapter 4: Expansions

Exercise 4.1Exercise 4.2

## 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.

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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.

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