Algebraic Expressions Test

Result

Algebraic Expressions Test - 14

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

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

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

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Algebraic Expressions Test - 14

Result

Algebraic Expressions Test - 14

Score

-

Rank

-

SHARING IS CARING

Question 1

$$y^2+y+15$$

$$5y^2-1$$

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

None of these

Solution

Question 2

$$5+4b-8$$

$$5a+4b-8$$

$$5a+4ab-8$$

$$5a+4b-10$$

Solution

Question 3

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

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

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

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

Solution

Question 4

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

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

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

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

Solution

Question 5

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

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

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

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

Solution

Question 6

$$x+18$$

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

$$-x+24$$

$$-9x+18$$

Solution

Question 7

$$\displaystyle -7-6x$$

$$\displaystyle -7+6x$$

$$\displaystyle 7+6x$$

$$\displaystyle 7-6x$$

Solution

Question 8

$$\displaystyle -4a+b$$

$$\displaystyle 4a-2b$$

$$0$$

$$\displaystyle -2b$$

Solution

Question 9

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

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

$$\displaystyle -12xy$$

$$\displaystyle 12xy$$

Solution

Question 10

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

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

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

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

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.