Algebraic Expressions Test

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Algebraic Expressions Test - 14

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Weekly Quiz Competition

Question 1
1 / -0

From $\displaystyle 8-y+{ 2y }^{ 2 }$ take away $\displaystyle \left( { y }^{ 2 }-7-2y \right)$ .

A
$y^2+y+15$

B
$5y^2-1$

C
$3y-7y^2+11$

D
None of these

Solution

Here we have to just subtract $y^2-7-2y$ from $8-y+2y^2$

$\therefore \displaystyle \left( 8-y+{ 2y }^{ 2 } \right) -\left( { y }^{ 2 }-7-2y \right) =8-y+{ 2y }^{ 2 }-{ y }^{ 2 }+7+2y$

$=\displaystyle \left( 8+7 \right) +\left( -y+2y \right) +\left( { 2y }^{ 2 }-{ y }^{ 2 } \right)$

$\displaystyle =15+y+{ y }^{ 2 }$

Hence, required value is $y^2+y+15$ .
Question 2
1 / -0

What should be subtracted from $2a+6b-5$ to get $-3a+2b+3$ ?

A
$5+4b-8$

B
$5a+4b-8$

C
$5a+4ab-8$

D
$5a+4b-10$

Solution

Let $X=-3a+2b+3$ and $Y=2a+6b-5$
Let $Z$ be the required expression
Now, $X=Y-Z$
$=>Z=Y-X$
Thus,
$2a+6b-5-(-3a+2b+3)$
$=2a+6b-5+3a-2b-3$
$=5a+4b-8$
Question 3
1 / -0

Find the sum of $\displaystyle { x }^{ 2 }-{ 2y }^{ 2 },{ 2x }^{ 2 }-4xy+{ 5y }^{ 2 },{ 6y }^{ 2 }+11xy-{ 6x }^{ 2 }$

A
$x^2-5xy+2y^2$

B
$5y^2+2xy-2x^2$

C
$9y^2+7xy-3x^2$

D
$2x^2-7xy+y^2$

Solution

Required sum $=\displaystyle { (x }^{ 2 }-{ 2y }^{ 2 })+{ (2x }^{ 2 }-4xy+{ 5y }^{ 2 })+{ (6y }^{ 2 }+11xy-{ 6x }^{ 2 })$

$=\displaystyle \left( { x }^{ 2 }+{ 2x }^{ 2 }-{ 6x }^{ 2 } \right) +\left( { -2y }^{ 2 }+{ 5y }^{ 2 }+{ 6y }^{ 2 } \right) +\left( -4xy+11xy \right)$ (Combining like terms)

$\displaystyle= -{ 3 }x^{ 2 }+{ 9y }^{ 2 }+7xy$ .
Question 4
1 / -0

What should be added to $5x^2+2xy+y^2$ to get $3x^2+4xy$ ?

A
$-2x^2+2xy-y^2$

B
$x^2+2y-y^2$

C
$-2x^2+2y-xy^2$

D
$x^2+2xy-y^2$

Solution

Let $A=3x^2+4xy$ and $B=5x^2+2xy+y^2$
Let $C$ be the required expression
Now, $A=B+C$
$=>C=A-B$
Thus, $3x^2+4xy-(5x^2+2xy+y^2)$
$=3x^2+4xy-5x^2-2xy-y^2$
$=-2x^2+2xy-y^2$
Question 5
1 / -0

Simplify
$\displaystyle \left ( a^{3}-2a^{2}+4a-5 \right )-\left ( -a^{3}-8a+2a^{2}+5 \right )$

A
$\displaystyle 2a^{3}+7a^{2}+6a-10$

B
$\displaystyle 2a^{3}+7a^{2}+12a-10$

C
$\displaystyle 2a^{3}-4a^{2}+12a-10$

D
$\displaystyle 2a^{3}+4a^{2}+6a-10$

Solution

$\displaystyle 3^{3}-2a^{2}+4a-5$
$\displaystyle (-)-a^{3}+2a^{2}-8a+5$
+ - + -
$\displaystyle \underline{\overline{2a^{3}-4a^{2}+12a-10}}$
Question 6
1 / -0

Subtract $(5x^{2}-5x-7)$ from the sum of $(x^{2}-3),\:(5-4x)$ and $(9+4x^{2})$

A
$x+18$

B
$x^{2}+x+10$

C
$-x+24$

D
$-9x+18$

Solution

$(x^2-3)+(5-4x)+(9+4x^2)=5x^2-4x+11$
Now, $(5x^2-4x+11)-(5x^2-5x-7)=x+18$
Option A is correct.
Question 7
1 / -0

Simplify : $\displaystyle 5x-\left[ 4x-\left\{ \left( 2x-5 \right) -3\left( 3x-4 \right) \right\} \right]$

A
$\displaystyle -7-6x$

B
$\displaystyle -7+6x$

C
$\displaystyle 7+6x$

D
$\displaystyle 7-6x$

Solution

$\displaystyle 5x-\left[ 4x-\left\{ \left( 2x-5 \right) -3\left( 3x-4 \right) \right\} \right]$
$=5x-4x+[(2x-5)-3(3x-4)]$
$=5x-4x+2x-5-9x+12$
$=7-6x$
Question 8
1 / -0

$\displaystyle -a-[a+\{ { a+b-2a-(a-2b)\} }-b]$ is equal to

A
$\displaystyle -4a+b$

B
$\displaystyle 4a-2b$

C
$0$

D
$\displaystyle -2b$

Solution

Given, $\displaystyle -a-[a+\{ { a+b-2a-(a-2b)\} }-b]$
= $\displaystyle -a-[a+\{ { a+b-2a-a+2b\} }-b]$
$\displaystyle =-a-[a+\{ { -2a+3b\} }-b]$
$\displaystyle =-a-\left[ a-2a+3b-b \right]$
$\displaystyle =-a-\left[ -a+2b \right]$
$\displaystyle =-a+a-2b$
$\displaystyle =-2b$ , which is simplified form of the given expression.
Question 9
1 / -0

By how much is $\displaystyle x^{4}-4x^{2}y^{2}+y^{4}$ less than $\displaystyle x^{4}+8x^{2}y^{2}+y^{4}$ ?

A
$\displaystyle -12x^{2}y^{2}$

B
$\displaystyle 12x^{2}y^{2}$

C
$\displaystyle -12xy$

D
$\displaystyle 12xy$

Solution

We have to find solution of
$( x^{4}+8x^{2}y^{2}+y^{4})$ $-(x^{4}-4x^{2}y^{2}+y^{4})$
Separating like terms and unlike terms, we get
$=$ $x^4 - x^4 +y^4 - y^4 +8x^2y^2-(-4x^2y^2)$
$=$ $8x^2y^2 + 4x^2y^2$
$=$ $12x^2y^2$
Question 10
1 / -0

Subtract the sum of $\displaystyle \left( { 5x }^{ 2 }-7x+4 \right)$ and $\displaystyle \left( 2x-{ 5x }^{ 3 }+1 \right)$ from $\displaystyle \left( { 3x }^{ 2 }-1+5x \right)$ .

A
$\displaystyle { 5x }^{ 3 }+{ 11x }^{ 2 }-5x+3$

B
$5x^3-2x^2+10x-6$

C
$\displaystyle { 3x }^{ 3 }+{ 11x }^{ 2 }+3x+5$

D
$\displaystyle { 11x }^{ 3 }+{ 3x }^{ 2 }+5x-3$

Solution

$3x^2 - 1 + 5x - [(5x^2-7x+4) + (2x-5x^3+1)]$
= $3x^2 - 1 +5x - [5x^2-5x+5- 5x^3]$
= $3x^2 - 1 +5x - 5x^2+5x-5 +5x^3$
= $-2x^2 + 10x -6 + 5x^3$
= $5x^3 -2x^2 + 10x - 6$

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Algebraic Expressions Test - 14

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Algebraic Expressions Test - 14

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Question 1

y2+y+15y^2+y+15y2+y+15

5y2−15y^2-15y2−1

3y−7y2+113y-7y^2+113y−7y2+11

None of these

Solution

Question 2

5+4b−85+4b-85+4b−8

5a+4b−85a+4b-85a+4b−8

5a+4ab−85a+4ab-85a+4ab−8

5a+4b−105a+4b-105a+4b−10

Solution

Question 3

x2−5xy+2y2x^2-5xy+2y^2x2−5xy+2y2

5y2+2xy−2x25y^2+2xy-2x^25y2+2xy−2x2

9y2+7xy−3x29y^2+7xy-3x^29y2+7xy−3x2

2x2−7xy+y22x^2-7xy+y^22x2−7xy+y2

Solution

Question 4

−2x2+2xy−y2-2x^2+2xy-y^2−2x2+2xy−y2

x2+2y−y2x^2+2y-y^2x2+2y−y2

−2x2+2y−xy2-2x^2+2y-xy^2−2x2+2y−xy2

x2+2xy−y2x^2+2xy-y^2x2+2xy−y2

Solution

Question 5

2a3+7a2+6a−10\displaystyle 2a^{3}+7a^{2}+6a-102a3+7a2+6a−10

2a3+7a2+12a−10\displaystyle 2a^{3}+7a^{2}+12a-102a3+7a2+12a−10

2a3−4a2+12a−10\displaystyle 2a^{3}-4a^{2}+12a-102a3−4a2+12a−10

2a3+4a2+6a−10\displaystyle 2a^{3}+4a^{2}+6a-102a3+4a2+6a−10

Solution

Question 6

x+18x+18x+18

x2+x+10x^{2}+x+10x2+x+10

−x+24-x+24−x+24

−9x+18-9x+18−9x+18

Solution

Question 7

−7−6x\displaystyle -7-6x−7−6x

−7+6x\displaystyle -7+6x−7+6x

7+6x\displaystyle 7+6x7+6x

7−6x\displaystyle 7-6x7−6x

Solution

Question 8

−4a+b\displaystyle -4a+b−4a+b

4a−2b\displaystyle 4a-2b4a−2b

000

−2b\displaystyle -2b−2b

Solution

Question 9

−12x2y2\displaystyle -12x^{2}y^{2}−12x2y2

12x2y2\displaystyle 12x^{2}y^{2}12x2y2

−12xy\displaystyle -12xy−12xy

12xy\displaystyle 12xy12xy

Solution

Question 10

5x3+11x2−5x+3\displaystyle { 5x }^{ 3 }+{ 11x }^{ 2 }-5x+35x3+11x2−5x+3

5x3−2x2+10x−65x^3-2x^2+10x-65x3−2x2+10x−6

3x3+11x2+3x+5\displaystyle { 3x }^{ 3 }+{ 11x }^{ 2 }+3x+53x3+11x2+3x+5

11x3+3x2+5x−3\displaystyle { 11x }^{ 3 }+{ 3x }^{ 2 }+5x-311x3+3x2+5x−3

Solution

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$y^2+y+15$

$5y^2-1$

$3y-7y^2+11$

$5+4b-8$

$5a+4b-8$

$5a+4ab-8$

$5a+4b-10$

$x^2-5xy+2y^2$

$5y^2+2xy-2x^2$

$9y^2+7xy-3x^2$

$2x^2-7xy+y^2$

$-2x^2+2xy-y^2$

$x^2+2y-y^2$

$-2x^2+2y-xy^2$

$x^2+2xy-y^2$

$\displaystyle 2a^{3}+7a^{2}+6a-10$

$\displaystyle 2a^{3}+7a^{2}+12a-10$

$\displaystyle 2a^{3}-4a^{2}+12a-10$

$\displaystyle 2a^{3}+4a^{2}+6a-10$

$x+18$

$x^{2}+x+10$

$-x+24$

$-9x+18$

$\displaystyle -7-6x$

$\displaystyle -7+6x$

$\displaystyle 7+6x$

$\displaystyle 7-6x$

$\displaystyle -4a+b$

$\displaystyle 4a-2b$

$0$

$\displaystyle -2b$

$\displaystyle -12x^{2}y^{2}$

$\displaystyle 12x^{2}y^{2}$

$\displaystyle -12xy$

$\displaystyle 12xy$

$\displaystyle { 5x }^{ 3 }+{ 11x }^{ 2 }-5x+3$

$5x^3-2x^2+10x-6$

$\displaystyle { 3x }^{ 3 }+{ 11x }^{ 2 }+3x+5$

$\displaystyle { 11x }^{ 3 }+{ 3x }^{ 2 }+5x-3$