Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

Simplify: $$\left (\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2} \right)$$.

A
$$3$$

B
$$5$$

C
$$6$$

D
$$8$$

Solution

Given, $$(\sqrt { 5 } +\sqrt { 2 } )(\sqrt { 5 } -\sqrt { 2 } )$$.

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

Applying the identity,

$$(\sqrt { 5 } +\sqrt { 2 } )(\sqrt { 5 } -\sqrt { 2 } )$$

$$=(\sqrt { 5 })^2- (\sqrt { 2 })^2=5-2=3$$.

Hence, $$(\sqrt { 5 } +\sqrt { 2 } )(\sqrt { 5 } -\sqrt { 2 } )=3$$.

Therefore, option $$A$$ is correct.
Question 2
1 / -0

Evaluate using expansion of $$(a+b)^2$$ or $$(a-b)^2$$ :
$$(9.4)^2$$

A
88.36

B
88.46

C
89.16

D
89.56

Solution

$${ (a+b) }^{ 2 }\quad =\quad a^{ 2 }+b^{ 2 }+2ab\\ a=9,\quad b=0.4\\ =\quad 9^{ 2 }+0.4^{ 2 }+2*9*0.4\\ =\quad 88.36$$
Question 3
1 / -0

Evaluate using expansion of $$(a+b)^2$$ or $$(a-b)^2$$ :
$$(188)^2$$

A
35444

B
35484

C
35344

D
35384

Solution

$$ {188}^{2} = {(200 - 12)}^{2} $$

It is the form of $$ {(a - b)}^{2} $$, where $$ a = 200, b = 12 $$

Applying the formula $$ { (a - b) }^{ 2 } = {a}^{2} + { b }^{ 2 } - 2ab $$
$$ {188}^{2} = {(200 - 12)}^{2} = {200}^{2} + { 12 }^{ 2 } - 2\times 200 \times 12 = 40000 + 144 - 4800 = 35344 $$
Question 4
1 / -0

Evaluate:
$$203\times 197$$

A
39991

B
39891

C
39981

D
38981

Solution

$$ 203 \times 197 = (200 + 3) \times (200 - 3) $$

Applying the formula $$ (a+b)(a-b) = { a }^{ 2 }-{ b }^{ 2 } $$, where $$ a =

200 , b = 3 $$

$$ 203 \times 197 = (200 + 3) \times (200 - 3) = { 200 }^{ 2 }-{ 3 }^{ 2 } = 40,000 - 9 = 39991 $$
Question 5
1 / -0

Evaluate:
$$20.8 \times 19.2$$

A
399.86

B
398.16

C
399.36

D
398.56

Solution

$$ 20.8 \times 19.2 = (20+ 0.8) \times (20 - 0.8) $$

Applying the formula $$ (a+b)(a-b) = { a }^{ 2 }-{ b }^{ 2 } $$, where $$ a =

20 , b = 0.8 $$

$$ 20.8 \times 19.2 = (20+ 0.8) \times (20 - 0.8) = { 20 }^{ 2 }-{ 0.8 }^{ 2 } = 400 - 0.64

= 399.36 $$
Question 6
1 / -0

Find the square of:
$$ 9.7$$

A
97.09

B
94.09

C
96.09

D
93.09

Solution

We can write
$$ {9.7}^{2} = {(10 - 0.3)}^{2} $$
It is the form of $$ {(a - b)}^{2} $$, where $$ a = 10, b = 0.3 $$
Applying the formula $$ { (a - b) }^{ 2 } = {a}^{2} + { b }^{ 2 } - 2ab$$
$$ {9.7}^{2} = {(10 - 0.3)}^{2} = {10}^{2} + { 0.3 }^{ 2 } -2\times 10 \times 0.3 = 100 + 0.09 - 6 = 94.09 $$
Question 7
1 / -0

Find the square of:
$$391 $$

A
154881

B
153881

C
152881

D
151881

Solution

$$ {391}^{2} = {(400 - 9)}^{2} $$

It is the form of $$ {(a - b)}^{2} $$, where $$ a = 400, b = 9 $$

Applying the formula $$ { (a - b) }^{ 2 } = {a}^{2} + { b }^{ 2 } - 2ab

$$
$$ {391}^{2} = {(400 - 9)}^{2} = {400}^{2} + { 9 }^{ 2 } -

2\times 400 \times 9 = 1,60,000 + 81 - 7200 = 152881 $$
Question 8
1 / -0

Find the square of: $$3a - 4b$$.

A
$$a^{2}\, +\, 4ab\, +\,b^{2}$$

B
$$9a^{2}\, -\, 24ab\, +\,16b^{2}$$

C
$$9a^{2}\, -\, ab\, +\,16b^{2}$$

D
$$9a^{2}\, +\, 24ab\, +\,b^{2}$$

Solution

Given, $$(3a-4b)$$.

On squaring, we get, $$(3a-4b)^2$$.

We know, $$(x+y)^2=x^2+y^2+2xy$$.

Then,
$$(3a-4b)^2$$
$$=(3a)^2-2(3a)(4b)+(4b)^2$$
$$=9a^2-24ab+16b^2$$.

Therefore, option $$B$$ is correct.
Question 9
1 / -0

Find the square of: $$(3a + 7b)$$.

A
$$9a^{2}\, +\, 12ab\, +\, 22b^{2}$$

B
$$9a^{2}\, +\, 2ab\, -\, 49b^{2}$$

C
$$9a^{2}\, +\, 42ab\, +\, 49b^{2}$$

D
$$9a^{2}\, -\, 42ab\, +\, 9b^{2}$$

Solution

Given, $$2a + b$$.

On squaring, we get, $$(2a+b)^2$$.

We know, $$(x+y)^2=x^2+y^2+2xy$$.

Then,
$$(2a+b)^2$$
$$=(2a)^2+b^2+2(2a)(b)$$
$$=4a^2+4ab+b^2$$.

Therefore, option $$D$$ is correct.
Question 10
1 / -0

Find the square of: $$2a + b$$.

A
$$4a^{2}\, -\, 4b\, +\, b^{3}$$

B
$$a^{2}\, +\, 4ab\, +\, b^{3}$$

C
$$a^{2}\, -\, 4b\, +\, b^{2}$$

D
$$4a^{2}\, +\, 4ab\, +\, b^{2}$$

Solution

Given, $$2a + b$$.

On squaring, we get, $$(2a+b)^2$$.

We know, $$(x+y)^2=x^2+y^2+2xy$$.

Then,
$$(2a+b)^2$$
$$=(2a)^2+b^2+2(2a)(b)$$
$$=4a^2+4ab+b^2$$.

Therefore, option $$D$$ is correct.

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Algebraic Expressions and Identities Test - 25

Result

Algebraic Expressions and Identities Test - 25

Score

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Rank

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SHARING IS CARING

Question 1

$$3$$

$$5$$

$$6$$

$$8$$

Solution

Question 2

88.36

88.46

89.16

89.56

Solution

Question 3

35444

35484

35344

35384

Solution

Question 4

39991

39891

39981

38981

Solution

Question 5

399.86

398.16

399.36

398.56

Solution

Question 6

97.09

94.09

96.09

93.09

Solution

Question 7

154881

153881

152881

151881

Solution

Question 8

$$a^{2}\, +\, 4ab\, +\,b^{2}$$

$$9a^{2}\, -\, 24ab\, +\,16b^{2}$$

$$9a^{2}\, -\, ab\, +\,16b^{2}$$

$$9a^{2}\, +\, 24ab\, +\,b^{2}$$

Solution

Question 9

$$9a^{2}\, +\, 12ab\, +\, 22b^{2}$$

$$9a^{2}\, +\, 2ab\, -\, 49b^{2}$$

$$9a^{2}\, +\, 42ab\, +\, 49b^{2}$$

$$9a^{2}\, -\, 42ab\, +\, 9b^{2}$$

Solution

Question 10

$$4a^{2}\, -\, 4b\, +\, b^{3}$$

$$a^{2}\, +\, 4ab\, +\, b^{3}$$

$$a^{2}\, -\, 4b\, +\, b^{2}$$

$$4a^{2}\, +\, 4ab\, +\, b^{2}$$

Solution

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