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 5 of 9 pages

Question 41. Subtract

7 x - 3 x^{2}

from

4 x + 8 x^{2}

−3x
11x2−5x
11x2
11x2−3x

Discuss Question

Answer: Option D. -> 11x2−3x
:
D

4 x + 8 x^{2}

7 x - 3 x^{2}

(-) (+)

____________

- 3 x + 11 x^{2}

Question 42. 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 expression to be subtracted be

y

.
Hence,

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

On rearranging the terms,

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

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

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

\Rightarrow y = - x^{3} - 4 x^{2} + 9 x - 3

So we have to subtarct

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

to get the required value.

Question 43. (a+b+c)(a+b-c) = ___________.

a2+2ab−c2
a2+4ab+b2−c2
a2+2ab+b2
a2+2ab+b2−c2

Discuss Question

Answer: Option D. -> a2+2ab+b2−c2
:
D

(a + b + c) (a + b - c) =

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

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

Question 44.

When we add $5 a^{2} b + 6 a b + 7 b c + 54$ and $14 a b + 8 b c + 16$ , we get:

$5 a^{2} b + 20 a b + 7 b c + 70$
$5 a^{2} b + 6 a b + 7 b c + 8 a c + 70$
$5 a^{2} b + 16 a b + 7 b c + 8 a c + 70$
$5 a^{2} b + 20 a b + 15 b c + 70$

Discuss Question

Answer: Option D. ->

5 a^{2} b + 20 a b + 15 b c + 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 45.

Subtract $(8 - 6 x + x^{2} - 7 x^{3} + x^{5})$ from $(x^{4} - 6 x^{3} + x^{2} - 3 x + 1)$ .

$- x^{5} + x^{4} + x^{3} + 3 x$
$- x^{5} + x^{4} + x^{3} - 7$
$- x^{5} + x^{4} + x^{3} + 3 x - 7$
$- x^{5} + x^{4} + 4 x^{3} + 3 x - 7$

Discuss Question

Answer: Option C. ->

- x^{5} + x^{4} + x^{3} + 3 x - 7

:
C

$\begin{matrix} x^{4} & - 6 x^{3} & + x^{2} & - 3 x & + 1 x^{5} & - 7 x^{3} & + x^{2} & - 6 x & + 8 (-) & (+) & (-) & (+) & (-) - x^{5} + x^{4} & + x^{3} & + 3 x & - 7 \end{matrix}$
$= (- x^{5} + x^{4} + x^{3} + 3 x - 7)$

Question 46.

What must be subtracted from $(x^{3} - 3 x^{2} + 5 x - 1)$ to get $(2 x^{3} + x^{2} - 4 x + 2)$ ?

$- x^{3} + 4 x^{2} + 9 x - 3$
$- x^{3} - 4 x^{2} + 6 x - 3$
$- x^{3} - 4 x^{2} + 9 x - 9$
$- x^{3} - 4 x^{2} + 9 x - 3$

Discuss Question

Answer: Option D. ->

- x^{3} - 4 x^{2} + 9 x - 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 47.

$997 \times 998 =$
___

Discuss Question

Answer: Option D. ->

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

$997 \times 998 = (1000 - 3) (1000 - 2)$
$= 1000^{2} - 3 \times 1000 - 2 \times 1000 + (- 3) (- 2)$
$= [1000000 - 5000 + 6] = 995006$

Question 48.

$(x + y) (x - y) (x^{2} + y^{2})$ = ___________.

$x^{3} - y^{3}$
$x^{3} + y^{3}$
$x^{4} + y^{4}$
$x^{4} - y^{4}$

Discuss Question

Answer: Option D. ->

x^{4} - y^{4}

:
D

$To simplify : (x + y) (x - y) (x^{2} + y^{2})$
Using the identity,
$(a + b) (a - b) = a^{2} - b^{2}$
we get,
$(x + y) (x - y) (x^{2} + y^{2})$
$= (x^{2} - y^{2}) (x^{2} + y^{2})$
Using the same identity again,
$where a = x^{2} and b = y^{2}$ ,
we get,
$(x^{2} - y^{2}) (x^{2} + y^{2})$
$= {(x^{2})}^{2} - {(y^{2})}^{2}$
$= x^{4} - y^{4}$

Question 49.

Simplify $(x + 3) (x + 5)$ .

$x^{2} + 6 x + 9$
$x^{2} + 8 x + 15$
$x^{2} + 9 x + 6$
$9 x^{2} + 6 x + 9$

Discuss Question

Answer: Option B. ->

x^{2} + 8 x + 15

:
B

To simplify: $(x + 3) (x + 5)$
Using the identity $[(x + a) (x + b)^{2} = x^{2} + (a + b) x + a b]$
we get,
$(x + 3) (x + 5) = x^{2} + (3 + 5) x + 3 \times 5 = x^{2} + 8 x + 15$