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Math Assignment Class VIII | Algebraic Identities Ch-7

 Mathematics Assignment  Class VIII 

Algebraic Identities

Download or Print, free assignment with answer key for  Class 8  on ALGEBRAIC IDENTITIES Important and extra questions that cover all topics of ALGEBRAIC IDENTITIES and is useful and helpful for the students.

Algebraic Identities required to solve this assignment

Students need to learn these algebraic identities before start this assignment

(a + b)2 = a2 + b2 + 2ab

(a - b)2 = a2 + b2 - 2ab

a2 - b2 = (a + b)(a - b)

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

MATHEMATICS ASSIGNMENT 
CLASS - 8 CHAPTER - 7
ALGEBRAIC IDENTITIES
Question 1

Expand:  equation 

Answer 3x2 + 2y+ 49 - 2equation xy + 14equation y - 14equation x

Question 2
Factorise: x2 – 3x - 54
Answer : (x - 6) (x - 9)

Question 3
Factorise : p2 – pq - 6q2.
Answer : (p + 2q)(p - 3q)

Question 4
Factorise : (-3x + 4y – 5)2.

Answer : 9x2 + 16y+ 25 - 24xy - 40y + 30x

Question 5
Simplify : (2x + 5y)2 – (2x - 5y)2 

Ans: 40xy


Question 6: Factorise: x2 - 3x - 28

Ans: (x - 7)(x + 4)


Question 7
Factorise : 9x2y – 24xy2 + 16y3

Answer : y(3x - 4y)2

Question 8
Factorise:  (176)2 - (24)2

Answer : 15200

Question 9
Evaluate : 211 ✖ 189 - 106 ✖ 94

Answer :29915

Question 10
If a + b + c = 12 and a2 + b2 + c2 = 64, find the value of ab + bc + ca

Ans: 40

Question 11
Factorise : 4a2 + b2 + 25c2 + 4ab - 10bc - 20ca
Answer :(2a + b - 5c)2

Question 12
Factorise: 25x2 + y2 + 9z2  - 10xy – 6yz + 30xz

Answer : (- 5x + y + 3z)2

Question 13
Factorise:  equation 

Answer equation

Question 14
Factorise:  equation

Answer equation

Question 15
Factorise : 9m2 - 30mn + 25n2) - 64x2    

Ans: (3m - 5n + 8x)(3m - 5n - 8x)


Question 16
Factorise:  4(x + y)2 – 28(x2 – y2) + 49(x – y)2

Answer : (-5x + 9y)2    or  (5x - 9y)2

Solution Hint :

4(x + y)2 – 28(x2 – y2) + 49(x – y)2

= [2(x + y)]2 – 2 x 2(x + y) x 7(x + y) + [7(x - y)]2

Using:  a2 - 2ab + b2 = (a - b)2 we get

= [2(x + y) – 7(x - y)]2.

= (2x + 2y - 7x + 7y)2.

= (- 5x + 9y)2  or  (5x - 9y)2


Question 17
Simplify :     equation  

Answer : 1.3

Solution Hint:
Above problem can be written as 

  equation 

equation 

equation

Question 18
Simplify :   equation 

Answer : 100

Solution Hint:
Above problem can be written as

=  equation 

equation 

equation 

equation
Question 19
equation 
Answer : 14

Solution Hint:

equation 
equation 
equation 
Squaring on both side we get

equation 
equation 

equation 

 equation 

equation 


Question 20

equation

Solution Hint
Above problem can be written as

equation 

equation 

equation 


Question 21
Find the value of  x if

x2 – 91 = 2.3 x 2.3 + 2 x 0.7 x 2.3 + 0.7 x 0.7

Ans: 10

Solution Hint

x2 – 91 = 2.3  2.3 + 2  0.7  2.3 + 0.7  0.7

            = (2.3)2 + 2  2.3  0.7 + (0.7)2 

            = (2.3 + 0.7)2  = (3)2  = 9

x2 – 91 = 9

        x2 = 9 + 91 = 100

        x   = 10


Question 22
If     equation  then find the value of     equation
Answer: 2

Solution Hint

equation 

equation
Taking Square root on both side we get

equation

equation

equation 
Taking Square root on both side we get

equation

Question 23
If   equation  and   equation  , then find the value of   equation   

Answer: 4266

Solution Hint 

equation 

equation 

equation 
equation 
equation 
equation 
equation

Question 24:  (5x - 3y + 1)2 - (5x + 3y - 1)2.

Answer:    - 60xy + 20x

Solution Hint

(5x - 3y + 1)2 - (5x + 3y - 1)2.

Using a2 – b2 = (a + b)(a - b) we get

 = (5x - 3y + 1+5x + 3y - 1)(5x - 3y + 1-5x - 3y + 1)

= (10x)(- 6y + 2) = - 60xy + 20x

Question 25: 

If 3p - 4q = 8 and pq = 2, find the value of  (3p - 4q)2.

Answer: 160

Solution Hint:

3p - 4q = 8

Squaring on both side we get

(3p – 4q)2 = 82

9p2 + 16q2 – 24pq = 64

9p2 + 16q2 – 24 🇽 2 = 64

9p2 + 16q2 – 48 = 64

9p2 + 16q2  = 64 + 48 = 112

(3p – 4q)2 = 9p2 + 16q2  + 24pq

                = 112 + 24 🇽 2  = 160


Question 26: 

Factorise : equation

Answer  equation

Question 27: 
If  5x - 2y = 7 and xy = 2, find the value of  (5x + 2y)2.

Answer : 129

Question 28: 
Factorise:   (64m2 – 144mn + 81n2) – 25p2

Answer : (8m - 9n + 5p)(8m - 9n - 5p)
Question 29: Simplify : (a- b2)(a+ b2) - (a- b2)2.

Answer 2b2(a + b)(a - b)

Question 30: Factorise: y2 + y - 30

Answer : (y + 6)(y - 5)

Question 31

If  equation,  then find the value of  equation 
Ans. 51





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