Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

$$-2x\times 10y\times -3z=$$

A
$$-60xyz$$

B
$$60xz$$

C
$$-60xz$$

D
$$60xyz$$

Solution

$$-2x\times 10y\times -3z= -2\times 10\times -3\times x\times y\times z$$
$$=60xyz$$
Question 2
1 / -0

$$-8yz\times -2xy=$$

A
$$16xyz$$

B
$$-16xy^2z$$

C
$$16xy^2z$$

D
$$-16x^2y^2z^2$$

Solution

$$-8yz\times -2xy = (-8\times -2)\times yz\times xy$$
$$= 16\times y^2zx=16xy^2z$$
Question 3
1 / -0

$$2xy\times 7yz\times 9xz$$

A
$$126xyz$$

B
$$126x^2y^2z^2$$

C
$$126xyz^2$$

D
$$126x^2yz^2$$

Solution

$$2xy\times 7yz\times 9xz= (2\times 7\times 9)\times xy\times yx\times xz$$
$$=126x^2y^2z^2$$
Question 4
1 / -0

Find the product of $$x^2yz\times xy^2z^3$$.

A
$$x^3y^3z^4$$

B
$$x^3y^3z^3$$

C
$$x^3y^4z^3$$

D
$$x^3y^3z$$

Solution

$$x^2yz\times xy^2z^3 = x^2\times y\times z\times x\times y^2\times z^3$$
$$x^2\times x\times y\times y^2\times z\times z^3=x^3y^3z^4$$
Question 5
1 / -0

Find the product $$(a+b)(a-2b)$$, when $$a=1$$, $$ b=2$$.

A
$$8$$

B
$$10$$

C
$$9$$

D
$$-9$$

Solution

$$=(a+b)(a-2b) =a\times a+b\times (-2b)+b\times a+a\times (-2b)$$
$$=a^2-2b^2-ab$$

$$a=1, b=2$$
$$=1-2\times 2^2-1\times 2$$
$$=-9$$
Question 6
1 / -0

Find the product $$\dfrac{x}{2}\times (2x+4xy+6z)$$.

A
$$2x^2+4x^2y+3xz$$

B
$$624x^2y+3xz$$

C
$$2x^2+2x^2y+6xz$$

D
$$x^2+2x^2y+3xz$$

Solution

$$\dfrac{x}{2} \times(2x+4xy+6x)$$
$$=\dfrac{x}{2}\times 2x+\dfrac{x}{2}\times 4xy+\dfrac{x}{2}\times 6z$$
$$=x^2+2x^2y+3xz$$
Question 7
1 / -0

Find the product $$12m\times (n+2p+3m)$$.

A
$$36m^2+12mn+12mp$$

B
$$36m^2+12mn+24mp$$

C
$$36m^2+mn+mp$$

D
$$m^2+12mn+24mp$$

Solution

$$12m(n+2p+3m)$$
$$=12m\times n +12 m\times 2p+12m\times 3m$$
$$= 12mn+24mp+36m^2$$
Question 8
1 / -0

Multiply $$\displaystyle \left((\frac{2}{5}x+y)(x+\frac{3}{5}y)\right)$$

A
$$\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2$$

B
$$\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{3}{5}xy$$

C
$$\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{31}{25}xy$$

D
$$\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{xy}{5}$$

Solution

$$((\dfrac{2}{5}x+y)(x+\dfrac{3}{5}y)$$

=$$\dfrac{2}{5}x^2+\dfrac{6}{25}xy+xy+\dfrac{3}{5}x^2$$

=$$\dfrac{2}{5}x^2+\dfrac{31}{25}xy+\dfrac{3}{5}y^2$$
Question 9
1 / -0

Find the product $$(x+4)(x^2+2x+1)$$

A
$$x^3+4x^2+9x+4$$

B
$$x^3+6x^2+9x+4$$

C
$$x^3+4x^2+8x+4$$

D
$$x^3+6x^2+8x+4$$

Solution

$$(x+4)(x^2+2x+1) = x\times(x^2+2x+1)+4(x^2+2x+1)$$
$$=x^3+2x^2+x+4x^2+8x+4$$
$$=x^3+6x^2+9x+4$$
Question 10
1 / -0

Which of the following is correct?

A
$$(x-y)^2=x^2+2xy-y^2$$

B
$$(x-y)^2=x^2-2xy+y^2$$

C
$$(x-y)^2=x^2-y^2$$

D
$$(x+y)^2=x^2+2xy-y^2$$

Solution

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

Then,
$$(x-y)^2$$
$$=x^2-2(x)(y)+y^2$$ $$= x^2-2xy+y^2$$.

To verify this, let us consider:
$$(x-y)^2$$ $$=(x-y)$$$$(x-y)$$
$$=x(x-y)-y(x-y)$$
$$=x^2-xy-yx+y^2$$
$$=x^2-xy-xy+y^2$$
$$=x^2-2xy+y^2$$.

Hence, $$(x-y)^2$$ $$= x^2-2xy+y^2$$

Therefore, option $$B$$ is correct.

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions and Identities Test - 32

Result

Algebraic Expressions and Identities Test - 32

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Rank

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SHARING IS CARING

Question 1

$$-60xyz$$

$$60xz$$

$$-60xz$$

$$60xyz$$

Solution

Question 2

$$16xyz$$

$$-16xy^2z$$

$$16xy^2z$$

$$-16x^2y^2z^2$$

Solution

Question 3

$$126xyz$$

$$126x^2y^2z^2$$

$$126xyz^2$$

$$126x^2yz^2$$

Solution

Question 4

$$x^3y^3z^4$$

$$x^3y^3z^3$$

$$x^3y^4z^3$$

$$x^3y^3z$$

Solution

Question 5

$$8$$

$$10$$

$$9$$

$$-9$$

Solution

Question 6

$$2x^2+4x^2y+3xz$$

$$624x^2y+3xz$$

$$2x^2+2x^2y+6xz$$

$$x^2+2x^2y+3xz$$

Solution

Question 7

$$36m^2+12mn+12mp$$

$$36m^2+12mn+24mp$$

$$36m^2+mn+mp$$

$$m^2+12mn+24mp$$

Solution

Question 8

$$\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2$$

$$\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{3}{5}xy$$

$$\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{31}{25}xy$$

$$\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{xy}{5}$$

Solution

Question 9

$$x^3+4x^2+9x+4$$

$$x^3+6x^2+9x+4$$

$$x^3+4x^2+8x+4$$

$$x^3+6x^2+8x+4$$

Solution

Question 10

$$(x-y)^2=x^2+2xy-y^2$$

$$(x-y)^2=x^2-2xy+y^2$$

$$(x-y)^2=x^2-y^2$$

$$(x+y)^2=x^2+2xy-y^2$$

Solution

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