Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 35

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$(a+b)^2-2(a-b)^2+(a-b)(a+b)$$ is:

A
$$4ab-b^2$$

B
$$2ab-b^2$$

C
$$3ab-b^2$$

D
$$6ab-2b^2$$

Solution

Given, $$(a+b)^2-2(a-b)^2+(a-b)(a+b)$$.

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

Then,
$$(a+b)^2-2(a-b)^2+(a-b)(a+b)$$
$$=(a^2+b^2+2ab)-2(a^2+b^2-2ab)+(a^2-b^2)$$
$$=a^2+b^2+2ab-2a^2-2b^2+ 4ab+a^2-b^2$$
$$=2a^2+b^2+6ab-2a^2-3b^2$$
$$=6ab-2b^2$$.

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

Find the value of $$1.05\times 0.95$$ using standard identity.

A
$$0.9985$$

B
$$0.9975$$

C
$$0.9875$$

D
$$0.9995$$

Solution

Given, $$1.05\times 0.95$$
$$=(1+0.05)(1-0.05)$$.

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

Then,
$$1.05\times 0.95$$
$$=(1+0.05)(1-0.05)$$
$$=1^2-(0.05)^2$$
$$=1-0.0025$$
$$=0.9975$$.

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

Find the value of $$1.03^2$$ using identity.

A
$$1.0409$$

B
$$1.0609$$

C
$$1.0009$$

D
$$1.0309$$

Solution

Given, $$1.03^2 = (1+0.03)^2$$.

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

Then,
$$1.03^2 = (1+0.03)^2$$
$$=1^2+(0.03)^2+2\times 1\times 0.03$$
$$=1+0.0009+0.06$$
$$=1.0609$$.

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

Find the value of $$2x\times 3x^3y^2\times3y^3z^2$$

A
$$18x^4y^5z^2$$

B
$$12x^4y^5z^2$$

C
$$18x^2y^6z^2$$

D
$$18x^4y^5z^3$$

Solution

$$2x\times 3x^3y^2\times3y^3z^2$$
$$=(2\times 3\times 3)(x\times x^3)(y^2\times y^3)(z^2)$$
$$=18x^4y^5z^2$$, use $$a^m\times a^n=a^{m+n}$$
Question 5
1 / -0

Find the value of $$199\times 201$$.

A
$$39989$$

B
$$40001$$

C
$$39999$$

D
$$400011$$

Solution

Given, $$199\times 201$$
$$ =(200-1)(200+1) $$.

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

Then,
$$199\times 201$$
$$ =(200-1)(200+1) $$
$$= 200^2-1^2$$
$$= 40000-1$$
$$=39999$$.

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

Find the value of $$(-2x^2)\times (-3y^2)\times (-6z^2)$$.

A
$$-36xyz$$

B
$$36xyz$$

C
$$-36x^2y^2z$$

D
$$-36x^2y^2z^2$$

Solution

$$-2x^2\times -3y^2\times -6z^2$$
$$=-2\times -3\times -6\times x^2\times y^2\times z^2$$
$$=-36x^2y^2z^2$$
Question 7
1 / -0

Find the value of $$(a+b)^2-(a-b)^2$$.

A
$$ab$$

B
$$2ab$$

C
$$3ab$$

D
$$4ab$$

Solution

Given, $$(a+b)^2-(a-b)^2$$.

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

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

Therefore, option $$D$$ is correct.
Question 8
1 / -0

Find the value of $$(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)$$.

A
$$abc$$

B
$$a^2+b^2+c^2$$

C
$$0$$

D
$$1$$

Solution

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

$$\therefore (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)$$
$$=(a^2-b^2)+(b^2-c^2)+(c^2-a^2)$$
$$=a^2-b^2+b^2-c^2+c^2-a^2$$
$$=0$$.

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

$$\left( 3-\sqrt { 7 } \right) \left( 3+\sqrt { 7 } \right) =$$?

A
$$4$$

B
$$2$$

C
$$6$$

D
$$8$$

Solution

Given, $$({3}-{\sqrt { 7 } })$$$$({3}+{\sqrt { 7 } })$$.

We know, $$(x-y)(x+y)$$ $$={x}^{2}-{y}^{2}$$.

Thus,
$$({3}-{\sqrt { 7 } })$$$$({3}+{\sqrt { 7 } })$$
$$={3}^{2}-{(\sqrt { 7 } )}^{2}$$
$$=9-7=2$$.

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

Using binomial identities, expand the following expression $$(t+3)^2$$

A
$$t^2-6t-9$$

B
$$t^2+6t-9$$

C
$$t^2+6t+9$$

D
$$t^2-6t+9$$

Solution

We need to expand $$(t+3)^2$$
We know that binomial identities for $$(a+b)^2=a^2+2ab+b^2$$
So, $$a = t, b = 3$$
$$=$$ $$t^2+2\times 3t+3^2$$
$$=$$ $$t^2+6t+9$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions and Identities Test - 35

Result

Algebraic Expressions and Identities Test - 35

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SHARING IS CARING

Question 1

$$4ab-b^2$$

$$2ab-b^2$$

$$3ab-b^2$$

$$6ab-2b^2$$

Solution

Question 2

$$0.9985$$

$$0.9975$$

$$0.9875$$

$$0.9995$$

Solution

Question 3

$$1.0409$$

$$1.0609$$

$$1.0009$$

$$1.0309$$

Solution

Question 4

$$18x^4y^5z^2$$

$$12x^4y^5z^2$$

$$18x^2y^6z^2$$

$$18x^4y^5z^3$$

Solution

Question 5

$$39989$$

$$40001$$

$$39999$$

$$400011$$

Solution

Question 6

$$-36xyz$$

$$36xyz$$

$$-36x^2y^2z$$

$$-36x^2y^2z^2$$

Solution

Question 7

$$ab$$

$$2ab$$

$$3ab$$

$$4ab$$

Solution

Question 8

$$abc$$

$$a^2+b^2+c^2$$

$$0$$

$$1$$

Solution

Question 9

$$4$$

$$2$$

$$6$$

$$8$$

Solution

Question 10

$$t^2-6t-9$$

$$t^2+6t-9$$

$$t^2+6t+9$$

$$t^2-6t+9$$

Solution

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