FRANK Solutions for Class 9 Maths Chapter 4 - Expansions

Learn to expand the given mathematical expressions with Frank Solutions for ICSE Class 9 Mathematics Chapter 4 Expansions. Practise the solutions to evaluate expressions without using the multiplication method. Also, revise the steps to find the cube of the given expression with the help of our chapter solutions.

Also, practise the Frank textbook solutions to relearn the methods for solving expansions-based problems. You can also solve related problems by accessing TopperLearning’s online sample question papers and previous years’ papers with solutions. And if you have trouble with difficult questions, get a response to your doubts on our ‘UnDoubt’ section.

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Chapter 4 - Expansions Exercise Ex. 4.1

Question 1

Expand the following:
(i) (a + 4) (a + 7)
(ii) (m + 8) (m - 7)
(iii) (x - 5) (x - 4)
(iv) (3x + 4) (2x - 1)
(v) (2x - 5) (2x + 5) (2x- 3)

Solution 1

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
        (V)
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Question 2

Expand the following:

a. (a + 3b)2

b. (2p - 3q)2

c. Frank Solutions Icse Class 9 Mathematics Chapter - Expansions 

d. (x - 3y - 2z)2

Solution 2

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 3

Find the squares of the following:

a. 9m - 2n

b. 3p -4q2

c. Frank Solutions Icse Class 9 Mathematics Chapter - Expansions 

d. (2a + 3b - 4c)

Solution 3

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 4
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Solution 4
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Question 5

Evaluate the following without multiplying:

a. (95)2

b. (103)2

c. (999)2

d. (1005)2

Solution 5

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 6

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

a. 399 x 401

b. 999 x 1001

c. 409 x 5.1

d. 15.9 x 16.1

Solution 6

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 7
If a - b = 10 and ab = 11; find a + b.
Solution 7
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Question 8
If x + y = 9, xy = 20;
find: (i) x - y,
(ii) x2 - y2.
Solution 8
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Question 9

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 9

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 10

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 10

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 11

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Question 12

If p + q = 8 and p - q = 4, find:
(i) pq,
(ii) p2 + q2

Solution 12

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 13

If m - n = 0.9 and mn = 0.36, find:

a. m + n,

b. m2 - n2.

Solution 13

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 14

If x + y = 1 and xy = -12; find
(i) x - y,
(ii) x2 - y2.

Solution 14

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 15

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 15

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 16

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 16

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 17

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

Solution 17

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 18

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

Solution 18

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 19

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

Solution 19

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 20

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

Solution 20

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 21

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

Solution 21

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Chapter 4 - Expansions Exercise Ex. 4.2

Question 1

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

    (v) Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 1

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
  (v)
  Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Question 2
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Solution 2
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Question 3
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Solution 3
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Question 4

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 4

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 5

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 5

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 6(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions 

Solution 6(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 6(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions 

Solution 6(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 7

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 7

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 8

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 8

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 9

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 9

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 10

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 10

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 11

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 12

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 12

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 13

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 13

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 14

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 14

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 15

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 15

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 16

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

Solution 16

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 17

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

Solution 17

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 18

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

Solution 18

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 19

If a + b = 5 and ab = 2, find a3 + b3.

Solution 19

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 20

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

Solution 20

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 21

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

Solution 21

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 22

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

Solution 22

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 23

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

Solution 23

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(a)

Simplify:

(4x + 5y)2 + (4x - 5y)2

Solution 24(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(b)

Simplify:

(7a +5b)2 - (7a - 5b)2

Solution 24(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(c)

Simplify:

(a + b)3 + (a - b)3

Solution 24(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(d)

Simplify:

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions 

Solution 24(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(e)

Simplify:

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

Solution 24(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(f)

Simplify:

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions 

Solution 24(f)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(g)

Simplify:

(2x + y)(4x2 - 2xy + y2)

Solution 24(g)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(h)

Simplify:

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions 

Solution 24(h)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(i)

Simplify:

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

Solution 24(i)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(j)

Simplify:

(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)

Solution 24(j)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(k)

Simplify:

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

Solution 24(k)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(l)

Simplify:

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

Solution 24(l)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(m)

Simplify:

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

Solution 24(m)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(n)

Simplify:

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

Solution 24(n)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 24(o)

Simplify:

(4m - 5n - 8)(4m - 5n + 5)

Solution 24(o)

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Question 25

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Solution 25

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions

Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions
Frank Solutions Icse Class 9 Mathematics Chapter - Expansions