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# 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:

Answer 3x2 + 2y+ 49 - 2 xy + 14 y - 14 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
Factorise: y2 + y - 30

Answer : (y + 6)(y - 5)

Question 6
Factorise:   (64m2 – 144mn + 81n2) – 25p2

Answer : (8m - 9n + 5p)(8m - 9n - 5p)

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

Question 8
Factorise:  (176)2 - (24)2

Question 9
Evaluate : 211 ✖ 189 - 106 ✖ 94

Question 10
If  5x - 2y = 7 and xy = 2, find the value of  (5x + 2y)2.

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:

Question 14
Factorise:

Question 15
Simplify : (a- b2)(a+ b2) - (a- b2)2.

Answer 2b2(a + b)(a - b)

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 :

Solution Hint:
Above problem can be written as

Question 18
Simplify :

Solution Hint:
Above problem can be written as

=

Question 19

Solution Hint:

Squaring on both side we get

Question 20

Solution Hint
Above problem can be written as

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       then find the value of

Solution Hint

Taking Square root on both side we get

Taking Square root on both side we get

Question 23
If     and     , then find the value of

Solution Hint

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

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.

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 :