FRANK Solutions for Class 9 Maths Chapter 4 - Expansions

FRANK Solutions for Class 9 Maths Chapter 4 - Expansions

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

        (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 Exercise Ex. 4.2

Question 1

    (v)

Solution 1

  (v)

 

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