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 3 of 9 pages

Question 21. Find the area of a rectangle whose length is

5 x y

units and breadth is

8 x y^{2}

units.

40x2y3 square units
40x2y2 square units
40xy3 square units
40xy square units

Discuss Question

Answer: Option A. -> 40x2y3 square units
:
A
Given:
Length of the rectangle =

5 x y

units
Breadth of the rectangle =

8 x y^{2}

units
Area of therectangle = length

\times

breadth

= 5 x y \times 8 x y^{2}

= 40 x^{2} y^{3}

square units
Hence, the area of therectangle is

40 x^{2} y^{3}

square units.

Question 22. A monomial multiplied by a monomial always gives a ________.

Monomial
Binomial
Trinomial
Constant

Discuss Question

Answer: Option A. -> Monomial
:
A
When wemultiply monomials, we firstmultiplythe coefficients and thenmultiplythe variables by adding the exponents. This will always give a monomial.
For example,

2 a b \times 2 b

4 a b^{2}

, which is a monomial.

Question 23. Using an identity expand :

(2 y + 5) (2 y + 5)

4y2+10y+25
4y2+20y+25
4y2+20y+15
y2+20y+25

Discuss Question

Answer: Option B. -> 4y2+20y+25
:
B
We know that,

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

Using the identity

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

(2 y + 5) (2 y + 5) = (2 y + 5)^{2}

= (2 y)^{2} + 2 (2 y) (5) + 5^{2}

= 4 y^{2} + 20 y + 25

Question 24. Add

(3 + 2 y - 5 y^{2} + 6 y^{3}), (- 8 + 3 y + 7 y^{3})

and

(5 - 6 y - 8 y^{3} + y^{2})

−3y−4y2+5y3
−y−3y2+5y3
−y−4y2+5y3
−y−4y2+6y3

Discuss Question

Answer: Option C. -> −y−4y2+5y3
:
C
To add :

(3 + 2 y - 5 y^{2} + 6 y^{3}), (- 8 + 3 y + 7 y^{3})

and

(5 - 6 y - 8 y^{3} + y^{2})

(- 8 + 3 y + 7 y^{3})

does not have the term with

y^{2}

. So, we add

0 y^{2}

and hence, the expression will be

(- 8 + 3 y + 0 y^{2} + 7 y^{3})

.
On adding there expressions, we get,

3 + 2 y - 5 y^{2} + 6 y^{3}

- 8 + 3 y + 0 y^{2} + 7 y^{3}

5 - 6 y + y^{2} - 8 y^{3} - -------------------- -

- 1 y - 4 y^{2} + 5 y^{3}

(3 + 2 y - 5 y^{2} + 6 y^{3}) + (- 8 + 3 y + 7 y^{3}) + (5 - 6 y - 8 y^{3} + y^{2}) = (- y - 4 y^{2} + 5 y^{3})

Question 25. When we add

5 a^{2} b + 6 a b + 7 b c + 54

and

14 a b + 8 b c + 16

, we get:

5a2b+20ab+7bc+70
5a2b+6ab+7bc+8ac+70
5a2b+16ab+7bc+8ac+70
5a2b+20ab+15bc+70

Discuss Question

Answer: Option D. -> 5a2b+20ab+15bc+70
:
D

5 a^{2} b + 6 a b + 7 b c + 54

14 a b + 8 b c + 16

________________________________

5 a^{2} b + 20 a b + 15 b c + 70

Question 26. What must be subtracted from

(x^{3} - 3 x^{2} + 5 x - 1)

to get

(2 x^{3} + x^{2} - 4 x + 2)

−x3+4x2+9x−3
−x3−4x2+6x−3
−x3−4x2+9x−9
−x3−4x2+9x−3

Discuss Question

Answer: Option D. -> −x3−4x2+9x−3
:
D
Let the unknown be

= y

(x^{3} - 3 x^{2} + 5 x - 1) - y = 2 x^{3} + x^{2} - 4 x + 2

\Rightarrow y = (x^{3} - 3 x^{2} + 5 x - 1) - (2 x^{3} + x^{2} - 4 x + 2)

x^{3} - 3 x^{2} + 5 x - 1

2 x^{3} + x^{2} - 4 x + 2

(-) (-) (+) (-)

____________________

- x^{3} - 4 x^{2} + 9 x - 3

So we have to subtract

(- x^{3} - 4 x^{2} + 9 x - 3)

to get the required value.

Question 27. The product of

(t + s^{2})

and

(t^{2} - s)

t3+s2t2−st−s3
t3+s2t2−st−s2
t3+s2t2−2st−s3
t3+t2−st−s3

Discuss Question

Answer: Option A. -> t3+s2t2−st−s3
:
A

(t + s^{2}) (t^{2} - s) = [t (t^{2} - s) + s^{2} (t^{2} - s)]

= t^{3} - t s + s^{2} t^{2} - s^{3}

= t^{3} + s^{2} t^{2} - s t - s^{3}

Question 28.

997 \times 998 =

___

Discuss Question

997 \times 998 = (1000 - 3) (1000 - 2)

= 1000^{2} - 3 \times 1000 - 2 \times 1000 + (- 3) (- 2)

= [1000000 - 5000 + 6] = 995006

Question 29. The area of a rectangle having length and width as

5 x y

and

9 y

respectively is

45 x y

True
False
5q2p
12pq2

Discuss Question

Answer: Option B. -> False
:
B
Area of a rectangle = length× width
Area =

5 x y \times 9 y

45 x y^{2}

Hence the given statement is false.

Question 30. Construct:
(i) 2 binomials with 3 variables.
(ii) 3 polynomials with 3 terms and 2 variables.
(iii) 2 trinomials with x as the only variable.
(iv) 3 binomials with x and y as variable. [4 MARKS]

Discuss Question

:
Application: 1Mark each