Algebraic Expressions And Identities(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

ALGEBRAIC EXPRESSIONS AND IDENTITIES MCQs

Total Questions : 88 | Page 4 of 9 pages

Question 31. Give three examples of the expressions:
(i) containing one variable
(ii) containing two variables
(iii) containing two terms. [4 MARKS]

Discuss Question

:
Concept: 1Mark
Application: 1Mark each

(i) 4 x; 5 x + 2; 4 x^{2} + 4 x + 2

(i i) x + y; 5 x - 3 y; 4 x^{2} y^{2} + 4 x^{2} y + 5 y + 2

(i i i) 5 x - 4 y; 4 a^{2} + 5 b^{2}; 10 y + 2

Question 32. Subtract (ap+bq-cr) from (a+b+c)(p+q+r) . [1 MARK]

Discuss Question

:
Concept: 1 Mark
(a + b + c)(p + q + r) - (ap + bq - cr)
= (ap + aq + ar + bp + bq + br + cp + cq + cr) - (ap + bq - cr)
Now,
= ap + aq + ar + bp + bq + br + cp + cq + cr - ap - bq + cr
= aq + ar + bp + br + cp + cq + 2cr

Question 33. Add the following:

a (a + b), b (b + c), c (a + c) a n d a^{2} + b^{2} + c^{2}

[2 MARKS]

Discuss Question

:
Concept: 1Mark
Application: 1 Mark

\Rightarrow a (a + b) + b (b + c) + c (a + c) + a^{2} + b^{2} + c^{2}

\Rightarrow a^{2} + a b + b^{2} + b c + c^{2} + c a + a^{2} + b^{2} + c^{2}

\Rightarrow 2 a^{2} + 2 b^{2} + 2 c^{2} + a b + b c + c a

Question 34. Find the volume of rectangular boxes with the following length, breadth and height respectively

(i) (a^{2}, a^{3}, a^{4})

(i i) (x^{2} y^{2}, x z, z^{4})

[2 MARKS]

Discuss Question

:
Concept: 1Mark
Application: 1 Mark
(i) Volume =

a^{2} \times a^{3} \times a^{4} = a^{9}

(ii) Volume =

x^{2} y^{2} \times x z \times z^{4} = x^{3} y^{2} z^{5}

Question 35. Find the distance travelled with the following pairs of monomials as their speed and time respectively:

(i) (25 a^{2} b^{2}, 50 b)

(i i) (12 a b c, 23 c d e)

(i i i) (5 c^{2} d^{2}, 4 a^{2} b^{2})

[3 MARKS]

Discuss Question

:
Concept: 1Mark
Application: 2Marks
Distance Travelled

= S p e e d \times T i m e

(i) Distance Travelled

= 25 a^{2} b^{2} \times 50 b = 1250 a^{2} b^{3}

(ii) Distance Travelled

= 12 a b c \times 23 c d e = 276 a b c^{2} d e

(iii) Distance Travelled

= 5 c^{2} d^{2} \times 4 a^{2} b^{2} = 20 a^{2} b^{2} c^{2} d^{2}

Question 36. Using the identities of algebraic expressions, Find :

(i) 102^{2}

(i i) 53^{2}

(i i i) 1001^{2}

[3 MARKS]

Discuss Question

:
Application: 1Mark each
Using the identity :

(a + b)^{2} = a^{2} + 2 a b + b^{2}

(i) (102)^{2}

\Rightarrow (100 + 2)^{2}

\Rightarrow (100)^{2} + (2)^{2} + 2 (100) (2)

\Rightarrow 10000 + 4 + 400

\Rightarrow 10404

(i i) (53)^{2}

\Rightarrow (50 + 3)^{2}

\Rightarrow (50)^{2} + (3)^{2} + 2 (50) (3)

\Rightarrow 2500 + 9 + 300

\Rightarrow 2809

(i i i) (1001)^{2}

\Rightarrow (1000 + 1)^{2}

\Rightarrow (1000)^{2} + (1)^{2} + 2 (1000) (1)

\Rightarrow 1000000 + 1 + 2000

\Rightarrow 1002001

Question 37. A rectangular box having length, breadth and height as

(a + b + c), (a^{2} + b^{2}) a n d (2 a + 2 b + 2 c)

respectively. Find the volume of the box. [4 MARKS]

Discuss Question

:
Concept: 1Mark
Application: 3Marks
Total volume =

(a + b + c) (a^{2} + b^{2}) (2 a + 2 b + 2 c)

= (a^{3} + a b^{2} + a^{2} b + b^{3} + c a^{2} + c b^{2}) (2 a + 2 b + 2 c)

= (2 a^{4} + 2 a^{3} b + 2 a^{3} c + 2 a^{2} b^{2} + 2 a b^{3} + 2 a b^{2} c + 2 a^{3} b + 2 a^{2} b^{2} + 2 a^{2} b c + 2 a b^{3} + 2 b^{4} + 2 b^{3} c + 2 a^{3} c + 2 a^{2} b c + 2 a^{2} c^{2} + 2 a b^{2} c + 2 b^{3} c + 2 b^{2} c^{2})

= (2 a^{4} + 4 a^{3} b + 4 a^{3} c + 4 a^{2} b^{2} + 4 a b^{3} + 4 a b^{2} c + 4 a^{2} b c + 2 b^{4} + 4 b^{3} c + 2 a^{2} c^{2} + 2 b^{2} c^{2})

Question 38. Add the following:

(i) 5 a^{2} b^{2} + 10 a b - 12 a^{2} + 15 b - 20

and

34 a b + 24 a^{2} + 22 b + 24

(i i) a b c + 6 b c d + a b d - 9 a b + 4 b c - 9 a - 43

and

4 a c d + 10 a c - 54 b - 32 c

(i i i) 5 b c + 9 a d - 3 c - 12

and

24 - 5 c - 5 b + 2 a b

[4 MARKS]

Discuss Question

:
Concept: 1Mark
Application: 1Mark each

(i) 5 a^{2} b^{2} + 10 a b - 12 a^{2} + 15 b - 20 + 34 a b + 24 a^{2} + 22 b + 24

= 5 a^{2} b^{2} + 44 a b + 12 a^{2} + 37 b + 4

(i i) a b c + 6 b c d + a b d - 9 a b + 4 b c - 9 a - 43 + 4 a c d + 10 a c - 54 b - 32 c

= a b c + 6 b c d + a b d - 9 a b + 4 b c - 9 a - 43 + 4 a c d + 10 a c - 54 b - 32 c

(i i i) 5 b c + 9 a d - 3 c - 12 + 24 - 5 c - 5 b + 2 a b

= 5 b c + 9 a d - 8 c + 12 - 5 b + 2 a b

Question 39. Find the value of

36^{2} - 35^{2} =

___

Discuss Question

:
Usingthe Identity

(x + a) (x - a) = x^{2} - a^{2}

We Put x = 36 and a = 35
(36 + 35) (36- 35) = (71) (1) = 71

Question 40. Simplify

(x y + y z)^{2} - 2 x^{2} y^{2} z

and find it's value when

x = - 1, y = 1

and

z = 2

3
4
-3
0

Discuss Question

Answer: Option C. -> -3
:
C

{(x y + y z)}^{2}

is in the form of

{(a + b)}^{2}

where

a = x y

and

b = y z .

Using

{(a + b)}^{2} = a^{2} + b^{2} + 2 a b,

{(x y + y z)}^{2} = x^{2} y^{2} + y^{2} z^{2} + {2 x z y}^{2} .

Therefore,

{(x y + y z)}^{2} - 2 x^{2} y^{2} z = x^{2} y^{2} + y^{2} z^{2} + 2 x z y^{2} - 2 x^{2} y^{2} z

Substitutingthe values of

x

y

and

z

in the above expression, we get

x^{2} y^{2} + y^{2} z^{2} + 2 x z y^{2} - 2 x^{2} y^{2} z

{(- 1)}^{2} {(1)}^{2} + {(1)}^{2} {(2)}^{2} + 2 (- 1) (2) {(1)}^{2} - 2 {(1)}^{2} {(1)}^{2} (2)

1 +4 - 4 - 4 = -3

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8th Grade > Mathematics

ALGEBRAIC EXPRESSIONS AND IDENTITIES MCQs

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