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

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Algebraic Expressions and Identities Test - 32

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Question 1

−60xyz-60xyz−60xyz

60xz60xz60xz

−60xz-60xz−60xz

60xyz60xyz60xyz

Solution

Question 2

16xyz16xyz16xyz

−16xy2z-16xy^2z−16xy2z

16xy2z16xy^2z16xy2z

−16x2y2z2-16x^2y^2z^2−16x2y2z2

Solution

Question 3

126xyz126xyz126xyz

126x2y2z2126x^2y^2z^2126x2y2z2

126xyz2126xyz^2126xyz2

126x2yz2126x^2yz^2126x2yz2

Solution

Question 4

x3y3z4x^3y^3z^4x3y3z4

x3y3z3x^3y^3z^3x3y3z3

x3y4z3x^3y^4z^3x3y4z3

x3y3zx^3y^3zx3y3z

Solution

Question 5

888

101010

999

−9-9−9

Solution

Question 6

2x2+4x2y+3xz2x^2+4x^2y+3xz2x2+4x2y+3xz

624x2y+3xz624x^2y+3xz624x2y+3xz

2x2+2x2y+6xz2x^2+2x^2y+6xz2x2+2x2y+6xz

x2+2x2y+3xzx^2+2x^2y+3xzx2+2x2y+3xz

Solution

Question 7

36m2+12mn+12mp36m^2+12mn+12mp36m2+12mn+12mp

36m2+12mn+24mp36m^2+12mn+24mp36m2+12mn+24mp

36m2+mn+mp36m^2+mn+mp36m2+mn+mp

m2+12mn+24mpm^2+12mn+24mpm2+12mn+24mp

Solution

Question 8

25x2+35y2\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^252​x2+53​y2

25x2+35y2+35xy\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{3}{5}xy52​x2+53​y2+53​xy

25x2+35y2+3125xy\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{31}{25}xy52​x2+53​y2+2531​xy

25x2+35y2+xy5\displaystyle \frac{2}{5}x^2+\frac{3}{5}y^2+\frac{xy}{5}52​x2+53​y2+5xy​

Solution

Question 9

x3+4x2+9x+4x^3+4x^2+9x+4x3+4x2+9x+4

x3+6x2+9x+4x^3+6x^2+9x+4x3+6x2+9x+4

x3+4x2+8x+4x^3+4x^2+8x+4x3+4x2+8x+4

x3+6x2+8x+4x^3+6x^2+8x+4x3+6x2+8x+4

Solution

Question 10

(x−y)2=x2+2xy−y2(x-y)^2=x^2+2xy-y^2(x−y)2=x2+2xy−y2

(x−y)2=x2−2xy+y2(x-y)^2=x^2-2xy+y^2(x−y)2=x2−2xy+y2

(x−y)2=x2−y2(x-y)^2=x^2-y^2(x−y)2=x2−y2

(x+y)2=x2+2xy−y2(x+y)^2=x^2+2xy-y^2(x+y)2=x2+2xy−y2

Solution

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$-60xyz$

$60xz$

$-60xz$

$60xyz$

$16xyz$

$-16xy^2z$

$16xy^2z$

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

$126xyz$

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

$126xyz^2$

$126x^2yz^2$

$x^3y^3z^4$

$x^3y^3z^3$

$x^3y^4z^3$

$x^3y^3z$

$8$

$10$

$9$

$-9$

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

$624x^2y+3xz$

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

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

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

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

$36m^2+mn+mp$

$m^2+12mn+24mp$

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

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

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

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

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

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

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

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

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

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

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

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