Chapter 4 : Expansions - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 4 - Expansions Excercise 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

        (V)
Question 2

Expand the following:

a. (a + 3b)2

b. (2p - 3q)2

c.   

d. (x - 3y - 2z)2

Solution 2

Question 3

Find the squares of the following:

a. 9m - 2n

b. 3p -4q2

c.   

d. (2a + 3b - 4c)

Solution 3

Question 4
Solution 4
Question 5

Evaluate the following without multiplying:

a. (95)2

b. (103)2

c. (999)2

d. (1005)2

Solution 5

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

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

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

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

Solution 12

Question 13

If m - n = 0.9 and mn = 0.36, find:

a. m + n,

b. m2 - n2.

Solution 13

Question 14

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

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

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

Solution 17

Question 18

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

Solution 18

Question 19

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

Solution 19

Question 20

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

Solution 20

Question 21

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

Solution 21

Chapter 4 - Expansions Excercise Ex. 4.2

Question 1

    (v) begin mathsize 12px style straight a minus 1 over straight a plus straight b end style

Solution 1

  (v)
  begin mathsize 12px style Using space left parenthesis straight a space plus space straight b space plus space straight c right parenthesis cubed equals straight a cubed plus straight b cubed plus straight c cubed plus 3 straight a squared straight b plus 3 straight a squared straight c plus 3 straight b squared straight a plus 3 straight c squared straight a plus 6 abc
open parentheses straight a minus 1 over straight a plus straight b close parentheses cubed
equals straight a cubed plus open parentheses negative 1 over straight a close parentheses cubed plus straight b cubed plus 3 straight a squared open parentheses negative 1 over straight a close parentheses plus 3 straight a squared plus 3 open parentheses negative 1 over straight a close parentheses squared straight b plus 3 open parentheses negative 1 over straight a close parentheses squared straight a plus 3 straight b squared straight a plus 3 straight b squared open parentheses negative 1 over straight a close parentheses plus 6 straight a open parentheses negative 1 over straight a close parentheses straight b
equals straight a cubed minus 1 over straight a cubed plus straight b cubed minus 3 straight a plus 3 straight a squared straight b plus fraction numerator 3 straight b over denominator straight a squared end fraction plus 3 over straight a plus 3 straight b squared straight a minus fraction numerator 3 straight b squared over denominator straight a end fraction minus 6 straight b end style
Question 2

Solution 2
Question 3

Solution 3
Question 4

Solution 4

Question 5

Solution 5

Question 6

  

Solution 6

Question 7

  

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

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

Solution 17

Question 18

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

Solution 18

Question 19

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

Solution 19

Question 20

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

Solution 20

Question 21

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

Solution 21

Question 22

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

Solution 22

Question 23

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

Solution 23

Question 24

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

Solution 24

Question 25

Simplify:

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

Solution 25

Question 26

Simplify:

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

Solution 26

Question 27

Simplify:

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

Solution 27

Question 28

Simplify:

  

Solution 28

Question 29

Simplify:

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

Solution 29

Question 30

Simplify:

  

Solution 30

Question 31

Simplify:

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

Solution 31

Question 32

Simplify:

  

Solution 32

Question 33

Simplify:

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

Solution 33

Question 34

Simplify:

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

Solution 34

Question 35

Simplify:

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

Solution 35

Question 36

Simplify:

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

Solution 36

Question 37

Simplify:

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

Solution 37

Question 38

Simplify:

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

Solution 38

Question 39

Simplify:

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

Solution 39

Question 40

Solution 40

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