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 8 of 9 pages

Question 71.

$Find the sum of$
$(11 x^{2} - 8 x + 4) and (6 x^{2} + 7 x - 10) .$

$17 x^{2} - x - 6$
$17 x^{2} - x + 6$
$17 x^{2} + x - 6$
$18 x^{2} - x - 6$

Discuss Question

Answer: Option A. ->

17 x^{2} - x - 6

:
A

$To find : Sum of (11 x^{2} - 8 x + 4) and (6 x^{2} + 7 x - 10)$
On adding the like terms together, we get,
$11 x^{2} - 8 x + 4$
$+ 6 x^{2} + 7 x - 10 - ---------------- -$
$17 x^{2} - x - 6$

Question 72.

Simplify:
${(x y + y z)}^{2} - {(x y - y z)}^{2}$

${4 x y}^{2}$
$4 x y^{2} z$
$4 x z$
$- 4 x y^{2} z$

Discuss Question

Answer: Option B. ->

4 x y^{2} z

:
B

Using the identity,
${(a + b)}^{2} = a^{2} + b^{2} + 2 a b,$
we get,
${(x y + y z)}^{2} = x^{2} y^{2} + y^{2} z^{2} + 2 x z y^{2} . . . (1)$
Using the identity,
${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$
we get,
${(x y - y z)}^{2} = x^{2} y^{2} + y^{2} z^{2} - 2 x z y^{2} . . . (2)$
Subtracting (2) from (1), we get

$(x^{2} y^{2} + y^{2} z^{2} + 2 x z y^{2}) - (x^{2} y^{2} + y^{2} z^{2} - 2 x z y^{2})$
$= 2 x z y^{2} + 2 x z y^{2}$
$= 4 x y^{2} z$

Question 73.

Find the value of $36^{2} - 35^{2} =$

___

Discuss Question

Answer: Option B. ->

4 x y^{2} z

Using the Identity $(x + a) (x - a) = x^{2} - a^{2}$
We Put x = 36 and a = 35

(36 + 35) (36 - 35) = (71) (1) = 71

Question 74.

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

Substituting the 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

Question 75.

Which of the following is a binomial?

2x + 7
4x + y + 2
7 - 3x + 4y
3x

Discuss Question

Answer: Option A. -> 2x + 7
:
A

A polynomial which involves two terms is called a binomial. For example, 3y + 9, 4a - 10 etc.

Question 76.

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

$a^{2} + 2 a b - c^{2}$
$a^{2} + 4 a b + b^{2} - c^{2}$
$a^{2} + 2 a b + b^{2}$
$a^{2} + 2 a b + b^{2} - c^{2}$

Discuss Question

Answer: Option D. ->

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

:
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 77.

Which of the following is an algebraic expression?

$\frac{x}{2} - 3$
4x + 7
3
x = 10

Discuss Question

Answer: Option D. -> x = 10
:
A, B, and C

An algebraic expression consists of variables, constants and operators (+, -, / ,x). An algebraic expression is the sum of algebraic terms.

When an algebraic expression is equated to another algebraic expression or zero, it becomes an algebraic equation.

$\frac{x}{2} - 3$ has the variable $x$ , constant term $3$ and the operator $^{'} -^{'}$ .

$4 x + 7$ has the variable $x$ , constant term $7$ and the operator $^{'} +^{'}$ .

$3$ can be written as $3 x^{0} + 0$ which has a variable term, constant term and the operator.

Hence, $\frac{x}{2} - 3, 4 x + 7$ and $3$ are algebraic expressions where as $x = 10$ is an algebraic equation.

Question 78.

$5 x \times (- 4 y z) \times 3 x z$ = ___

$60 x y z$
$15 x^{2}$ $z^{2} - 4 y z$
$- 60 x y z$
$- 60 x^{2} y z^{2}$

Discuss Question

Answer: Option D. ->

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

:
D

On multiplying $x$ with $x$ , its power is raised to 2 i.e., $x \times x = x^{2}$
On multiplying $z$ with $z$ its power is also raised to 2 .
i.e.,
$z \times z = z^{2}$
Multiply all the coefficients to get $5 \times (- 4) \times 3 = - 60$

Therefore, the answer is $- 60 x^{2} y z^{2}$ .

Question 79.

When $7 x y + 5 y z - 3 z x,$ $4 y z + 9 z x - 4 y$ and $- 3 x z + 5 x - 2 x y$ are added, we get ___.

$5 x y + 9 y z + 3 z x + 5 x - 4 y$
$5 x y + 9 y z + 15 z x + 5 x - 4 y$
$5 x y + 9 y z - 3 z x + 5 x - 4 y$
$5 x y + 9 y z + 3 z x - 5 x - 4 y$

Discuss Question

Answer: Option A. ->

5 x y + 9 y z + 3 z x + 5 x - 4 y

:
A

7 x y + 5 y z - 3 z x

4 y z + 9 z x - 4 y

- 2 x y - 3 x z + 5 x

________________________

5 x y + 9 y z + 3 z x - 4 y + 5 x

Question 80.

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

$x^{3} - 2 x^{2} - 8 x + 7$
$7 x^{3} + 2 x^{2} - 8 x + 7$
$7 x^{3} - 2 x^{2} - 8 x + 3$
$7 x^{3} - 2 x^{2} - 8 x + 7$

Discuss Question

Answer: Option D. ->

7 x^{3} - 2 x^{2} - 8 x + 7

:
D

$4 x^{3} - 3 x + 5$
$- 3 x^{3} + 5 x - 2 + 2 x^{2}$
$(+) (-) (+) (-)$
________________________
$7 x^{3} - 8 x + 7 - 2 x^{2}$
$= 7 x^{3} - 2 x^{2} - 8 x + 7$