Algebraic Expressions and Identities Test

Result

Algebraic Expressions and Identities Test - 30

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Multiply the binomials $$(2x + 5)$$ and $$(4x - 3)$$

A
$$ 8x^2+ 14x -15$$

B
$$ 7x^2-14x -15$$

C
$$ x^2+ 14x -18$$

D
None of these

Solution

$$(2x + 5)\times (4x - 3)= 2x(4x - 3) + 5(4x - 3)$$
$$ = 8x^2- 6x + 20x-15$$
$$ = 8x^2+ 14x -15$$
Question 2
1 / -0

Using identities, evaluate $$8.9^2$$.

A
$$74.53$$

B
$$73.42$$

C
$$79.21$$

D
$$73.21$$

Solution

Given, $$8.9^2$$
$$= (9 -0.1)^2$$.

We know, $$(a-b)^2 =a^2-2ab+b^2$$.

Then,
$$8.9^2$$
$$= (9 -0.1)^2$$
$$ = (9)^2 -2(9) (0.1) + (0.1)^2$$
$$ = 81 -1.8 + 0.01 = 79.20+0.01=79.21$$.

Therefore, option $$C$$ is correct.
Question 3
1 / -0

Using identities, evaluate $$12.1^2 -7.9^2$$.

A
$$84$$

B
$$72$$

C
$$69$$

D
$$87$$

Solution

Given, $$(12.1)^2-(7.9)^2$$.

We know, $$(a^2-b^2)=(a+b)(a-b)$$.

Then,
$$(12.1)^2-(7.9)^2$$

$$=(12.1+7.9)(12.1-7.9)$$

$$=20\times 4.2$$

$$=84$$.

Therefore, option $$A$$ is correct.
Question 4
1 / -0

Using $$(x + a) (x + b) = x^2+(a+b)x+ab$$, find $$103 \times 104$$.

A
$$14982$$

B
$$11992$$

C
$$10712$$

D
$$11482$$

Solution

Given, $$103 \times 104 $$
$$=(100+3)(100+4)$$.

Using, $$ (x+a)(x+b)=x^2+(a+b)x+ab$$.

Then,
$$103 \times 104 $$
$$=(100+3)(100+4)$$
$$ =(100)^2+(3+4)(100) +(3)(4)$$
$$ =(100)^2+(7)(100) +12$$
$$ = 10000 +700 + 12$$
$$ = 10712$$.

Therefore, option $$C$$ is correct.
Question 5
1 / -0

Simplify: $$(7m -8n)^2 + (7m + 8n)^2$$.

A
$$49m^2+164n^2$$

B
$$98m^2+128n^2$$

C
$$49m^2+64n^2$$

D
$$128m^2+64n^2$$

Solution

Given, $$(7m -8n)^2 + (7m + 8n)^2$$.

We know, $$(a-b)^2=a^2-2ab+b^2$$
and $$(a+b)^2=a^2+2ab+b^2$$.

Then,
$$(7m -8n)^2 + (7m + 8n)^2$$
$$ = ((7m)^2-2(7m)(8n) + (8n)^2)+((7m)^2 + 2(7m)(8n) + (8n)^2)$$
$$ = (49m^2-112mn + 64n^2)+(49m^2 + 112mn + 64n^2)$$
$$ = 49m^2-112mn + 64n^2+49m^2 + 112m + 64n^2$$
$$ = 98m^2 + 128n^2$$.

Therefore, option $$B$$ is correct.
Question 6
1 / -0

Using identities, evaluate $$5.2^2$$.

A
$$26.04$$

B
$$2704$$

C
$$27.04$$

D
$$2604$$

Solution

Given, $$(5.2)^2$$

We know, $$(a+b)^2=a^2+b^2+2ab$$.

Then,
$$(5.2)^2$$
$$=(5+0.2)^2$$
$$=5^2+(0.2)^2+2(5)(0.2)$$
$$=25+0.04+2(1)$$
$$=25+0.04+2$$
$$=27.04$$.

Therefore, option $$C$$ is correct.
Question 7
1 / -0

Simplify $$(x^2-5)(x+5)+ 25$$

A
$$ x^2(x+5) -5(x+5)+15$$

B
$$ x^2(x+5) -5(x-5)+25$$

C
$$ x^2(x+5) -5(x+5)+25$$

D
$$ x^2(x+5) -(x+5)+25$$

Solution

Given, $$(x^2-5)(x + 5) + 25$$

While multiplying a binomial with another binomial, each term of the first binomial must be multiplied by each term of the second binomial.

$$ = x^2(x+5) -5(x+5)+25$$
Question 8
1 / -0

Simplify: $$(a^2 + 5)(b^3 + 3) + 5$$

A
$$ a^3(b^3+3)+ 5(b^3 + 3)+ 5$$

B
$$ a^2(b^3+3)+ 5(b^3 + 3)+ 5$$

C
$$ a^3(b^3+3)+ 5(b^3 + 3)- 5$$

D
$$ a^2(b^3+3)+ 5(b^3 - 3)+ 5$$

Solution

$$(a^2+ 5)(b^3+ 3) + 5$$
$$ = a^2(b^3+3)+ 5(b^3 + 3)+ 5$$
$$ = a^2b^3+ 3a^2+ 5b^3+ 15 + 5$$
$$ = a^2b^3 + 3a^2+ 5b^3+ 20$$
Question 9
1 / -0

$$3x \times (4x + 2)$$

A
$$12x^{2} + 6x$$

B
$$6 (2x^{2} + x)$$

C
$$x (12x + 6)$$

D
All of the above

Solution

$$3x \times (4x + 2)$$
$$= 12x^{2} + 6x$$
Hence option A is correct.

$$3x \times (4x + 2)$$
$$=3x \times 2 (2x+1)$$
$$=6(2x^2+x)$$
Hence option B is correct.

$$3x \times (4x + 2)$$
$$= 12x^{2} + 6x$$
$$=x(12x+6)$$
Hence option C is correct.
Question 10
1 / -0

$$(4x + 1)(4x - 1) =$$

A
$$16x^{2} + 8x + 2$$

B
$$16x^{2} + 8x + 1$$

C
$$16x^{2} - 1$$

D
$$16x^{2} + 1$$

Solution

Given that: $$ (4x+1)\times(4x-1)$$
We can see that: $$ (4x+1)\times(4x-1)=$$ $$ 4x\times(4x-1)+1\times (4x-1)$$
$$\Rightarrow (4x\times 4x)-(4x\times 1)+(1\times 4x)-(1\times 1)$$
$$\Rightarrow 16x^2-4x+4x-1$$
$$\Rightarrow 16x^2-1$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Algebraic Expressions and Identities Test - 30

Result

Algebraic Expressions and Identities Test - 30

Score

-

Rank

-

SHARING IS CARING

Question 1

$$ 8x^2+ 14x -15$$

$$ 7x^2-14x -15$$

$$ x^2+ 14x -18$$

None of these

Solution

Question 2

$$74.53$$

$$73.42$$

$$79.21$$

$$73.21$$

Solution

Question 3

$$84$$

$$72$$

$$69$$

$$87$$

Solution

Question 4

$$14982$$

$$11992$$

$$10712$$

$$11482$$

Solution

Question 5

$$49m^2+164n^2$$

$$98m^2+128n^2$$

$$49m^2+64n^2$$

$$128m^2+64n^2$$

Solution

Question 6

$$26.04$$

$$2704$$

$$27.04$$

$$2604$$

Solution

Question 7

$$ x^2(x+5) -5(x+5)+15$$

$$ x^2(x+5) -5(x-5)+25$$

$$ x^2(x+5) -5(x+5)+25$$

$$ x^2(x+5) -(x+5)+25$$

Solution

Question 8

$$ a^3(b^3+3)+ 5(b^3 + 3)+ 5$$

$$ a^2(b^3+3)+ 5(b^3 + 3)+ 5$$

$$ a^3(b^3+3)+ 5(b^3 + 3)- 5$$

$$ a^2(b^3+3)+ 5(b^3 - 3)+ 5$$

Solution

Question 9

$$12x^{2} + 6x$$

$$6 (2x^{2} + x)$$

$$x (12x + 6)$$

All of the above

Solution

Question 10

$$16x^{2} + 8x + 2$$

$$16x^{2} + 8x + 1$$

$$16x^{2} - 1$$

$$16x^{2} + 1$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.