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 9 of 9 pages

Question 81.

Add $(3 + 2 y - 5 y^{2} + 6 y^{3}), (- 8 + 3 y + 7 y^{3})$ and $(5 - 6 y - 8 y^{3} + y^{2})$ .

$- 3 y - 4 y^{2} + 5 y^{3}$
$- y - 3 y^{2} + 5 y^{3}$
$- y - 4 y^{2} + 5 y^{3}$
$- y - 4 y^{2} + 6 y^{3}$

Discuss Question

Answer: Option C. ->

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

:
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 82.

${(1.05)}^{2} - {(0.95)}^{2} =$ ___

Discuss Question

Answer: Option C. ->

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

Using the identity
${(a)}^{2} - {(b)}^{2}$ $= (a + b) (a - b)$ ,
${(1.05)}^{2} - {(0.95)}^{2}$
$= (1.05 + 0.95) (1.05 - 0.95)$
$= (2) (0.1) = 0.2$

Question 83.

${(4 p q + 3 q)}^{2} - {(4 p q - 3 q)}^{2} =$ ____________.

$44 p q^{2}$
$48 p^{2} q$
$48 p q^{2}$
$44 p^{2} q$

Discuss Question

Answer: Option C. ->

48 p q^{2}

:
C

${(4 p q + 3 q)}^{2} - {(4 p q - 3 q)}^{2}$
We have:
$(a + b)^{2} = a^{2} + 2 a b + b^{2} (a - b)^{2} = a^{2} - 2 a b + b^{2}$
So, ${(4 p q + 3 q)}^{2} - {(4 p q - 3 q)}^{2}$
$= [{(4 p q)}^{2} + {(3 q)}^{2} + 2 (4 p q) (3 q)] - [{(4 p q)}^{2} + {(3 q)}^{2} - 2 (4 p q) (3 q)]$
$= 24 p q^{2} + 24 p q^{2}$
$= 48 p q^{2}$

Question 84.

Using an identity expand :
$(2 y + 5) (2 y + 5)$

$4 y^{2} + 10 y + 25$
$4 y^{2} + 20 y + 25$
$4 y^{2} + 20 y + 15$
$y^{2} + 20 y + 25$

Discuss Question

Answer: Option B. ->

4 y^{2} + 20 y + 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 85.

A monomial multiplied by a monomial always gives a ________.

Monomial
Binomial
Trinomial
Constant

Discuss Question

Answer: Option A. -> Monomial
:
A

When we multiply monomials, we first multiply the coefficients and then multiply the 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 86.

The numerical factor of a term is known as

Expression
Coefficient
Variable
Equation

Discuss Question

Answer: Option B. -> Coefficient
:
B

The numerical factor of a term is known as coefficient.

Question 87.

Simplify $(3 x^{2} + 5 y^{2}) (4 x y - 5 y)$ .

$(6 x^{3} y - 15 x y + 20 x y^{3} - 5 y^{3})$
$(12 x^{3} y - 5 x^{2} y + 10 x y^{3} + 25 y^{3})$
$(12 x^{3} y - 15 x^{2} y + 20 x y^{3} - 25 y^{3})$
$(6 x^{3} y - 15 x^{2} y + 10 x y^{3} - 5 y^{3})$

Discuss Question

Answer: Option C. ->

(12 x^{3} y - 15 x^{2} y + 20 x y^{3} - 25 y^{3})

:
C

Given: $(3 x^{2} + 5 y^{2}) (4 x y - 5 y)$
$= 3 x^{2} (4 x y - 5 y) + 5 y^{2} (4 x y - 5 y)$
$= 12 x^{3} y - 15 x^{2} y + 20 x y^{3} - 25 y^{3}$

Question 88.

Find the area of a rectangle whose length is $5 x y$ units and breadth is $8 x y^{2}$ units.

$40 x^{2}$ $y^{3}$ square units
$40 x^{2}$ $y^{2}$ square units
$40 x y^{3}$ square units
$40 x y$ square units

Discuss Question

Answer: Option A. ->

40 x^{2}

y^{3}

square units
:
A

Given:
Length of the rectangle = $5 x y$ units
Breadth of the rectangle = $8 x y^{2}$ units
Area of the rectangle = length $\times$ breadth
$= 5 x y \times 8 x y^{2}$
$= 40 x^{2} y^{3}$ square units
Hence, the area of the rectangle is $40 x^{2} y^{3}$ square units.