### Mathematics Class 10 Lab Manual | 21 Lab Activities

Mathematics Lab Manual Class X   lab activities for class 10 with complete observation Tables strictly according to the CBSE syllabus also very useful & helpful for the students and teachers.

# 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:  $\left(\sqrt{3}x-\sqrt{2}y-7\right)^{2}$

Answer 3x2 + 2y+ 49 - 2$\sqrt{6}$ xy + 14$\sqrt{2}$ y - 14$\sqrt{3}$ 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

Question 8
Factorise:  (176)2 - (24)2

Question 9
Evaluate : 211 ✖ 189 - 106 ✖ 94

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:  $a^{2}+4b^{2}+\frac{c^{2}}{9}+4ab-\frac{4bc}{3}-\frac{2ca}{3}$

Answer $\left(a+2b-\frac{c}{3}\right)^{2}$

Question 14
Factorise:  $a^{2}+\frac{1}{25}b^{2}+\frac{c^{2}}{4}-\frac{2}{5}ab-\frac{1}{5}bc+ca$

Answer $\left(a-\frac{b}{5}+\frac{c}{2}\right)^{2}$

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 :     $\frac{2.3\times 2.3-0.3\times 0.3}{2.3\times 2.3-2\times 2.3\times 0.3+0.3\times 0.3}$

Solution Hint:
Above problem can be written as

$\frac{(2.3)^{2}-(0.3)^{2}}{(2.3)^{2}-2\times 2.3\times 0.3+(0.3)^{2}}$

$=\frac{(2.3+0.3)(2.3-0.3)}{(2.3-0.3)^{2}}$

$=\frac{2.6\times 2}{2^{2}}=\frac{2.6}{2}=1.3$

Question 18
Simplify :   $\frac{8.63\times 8.63-1.37\times 1.37}{0.726}$

Solution Hint:
Above problem can be written as

=  $\frac{(8.63)^{2}-(1.37)^{2}}{0.726}$

$=\frac{(8.63+1.37)(8.63-1.37)}{0.726}$

$=\frac{10\times 7.26}{0.726}=\frac{72.6}{0.726}$

$=\frac{726}{726}\times\frac{1000}{10}=100$
Question 19
$Find\:\:\left(a^{4}+\frac{1}{a^{4}}\right)\:\:if\:\:\left(a+\frac{1}{a}\right)^{2}=6$

Solution Hint:

$\left(a+\frac{1}{a}\right)^{2}=6$
$a^{2}+\frac{1}{a^{2}}+2\times a\times\frac{1}{a}=6$
$a^{2}+\frac{1}{a^{2}}=6-2=4$
Squaring on both side we get

$\left(a^{2}+\frac{1}{a^{2}}\right)^{2}=4^{2}$
$a^{4}+\frac{1}{a^{4}}+2\times a^{2}\times\frac{1}{a^{2}}=16$

$a^{4}+\frac{1}{a^{4}}+2=16$

$a^{4}+\frac{1}{a^{4}}=16-2=14$

$a^{4}+\frac{1}{a^{4}}=14$

Question 20

$Simplify:\;\:\frac{2.5\times 2.5-0.2\times 0.2}{2.5\times 2.5-2\times 2.5\times 0.2+0.2\times 0.2}$

Solution Hint
Above problem can be written as

$\frac{(2.5)^{2}-(0.2)^{2}}{(2.5)^{2}-2\times 2.5\times 0.2+(0.2)^{2}}$

$=\frac{(2.5-0.2)(2.5+0.2)}{(2.5-0.2)^{2}}$

$=\frac{(2.5+0.2)}{(2.5-0.2)}=\frac{2.7}{2.3}=\frac{27}{23}$

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     $x^{4}+\frac{1}{x^{4}}=2,$  then find the value of     $x+\frac{1}{x}$

Solution Hint

$\left(x^{2}+\frac{1}{x^{2}}\right)^{2}=x^{4}+\frac{1}{x^{4}}+2$

$\left(x^{2}+\frac{1}{x^{2}}\right)^{2}=2+2=4$
Taking Square root on both side we get

$x^{2}+\frac{1}{x^{2}}=2$

$\left(x+\frac{1}{x}\right)^{2}=x^{2}+\frac{1}{x^{2}}+2$

$\left(x+\frac{1}{x}\right)^{2}=2+2=4$
Taking Square root on both side we get

$x+\frac{1}{x}=2$

Question 23
If   $x+\frac{1}{x}=9$  and   $x-\frac{1}{x}=6$  , then find the value of   $x^{4}-\frac{1}{x^{4}}$

Solution Hint

$\left(x+\frac{1}{x}\right)^{2}=9^{2}$

$x^{2}+\frac{1}{x^{2}}+2\times x\times\frac{1}{x}=81$

$x^{2}+\frac{1}{x^{2}}=81-2=79$
$x^{2}-\frac{1}{x^{2}}=\left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)$
$x^{2}-\frac{1}{x^{2}}=9\times 6=54$
$x^{4}-\frac{1}{x^{4}}=\left(x^{2}+\frac{1}{x^{2}}\right)\left(x^{2}-\frac{1}{x^{2}}\right)$
$x^{4}-\frac{1}{x^{4}}=79\times 54=4266$

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 ðŸ‡½ 2 = 64

9p2 + 16q2 – 48 = 64

9p2 + 16q2  = 64 + 48 = 112

(3p – 4q)2 = 9p2 + 16q2  + 24pq

= 112 + 24 ðŸ‡½ 2  = 160

Question 26:

Factorise : $5x^{2}+7y^{2}+z^{2}-2\sqrt{35}xy-2\sqrt{7}yz+2\sqrt{5}zx$

Answer  $(\sqrt{5}x-\sqrt{7}y+z)^{2}$

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

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  $x-\frac{1}{x}=7$,  then find the value of  $x-\frac{1}{x}=7$
Ans. 51