Algebraic Expressions Test

Result

Algebraic Expressions Test - 10

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

$$\displaystyle \left( p+q \right) -\left( p-q \right) $$ is equal to

A
$$\displaystyle 2p+2q$$

B
$$\displaystyle 2p$$

C
$$\displaystyle 2q$$

D
$$0$$

Solution

Given,
$$\displaystyle \left( p+q \right) -\left( p-q \right) =p+q-p+q$$
$$=2q$$
Hence simplified form of the given expression is $$2q$$
Question 2
1 / -0

$$\displaystyle { a }^{ 2 }-\left( -{ a }^{ 2 } \right) $$ is equal to

A
$$\displaystyle { 2a }^{ 2 }$$

B
$$\displaystyle { a }^{ 2 }$$

C
0

D
$$\displaystyle { -2a }^{ 2 }$$

Solution

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

Subtract the sum of $$\displaystyle { 9b }^{ 2 }+{ 3c }^{ 2 }$$ and $$\displaystyle { 2b }^{ 2 }+bc+{ 2c }^{ 2 }$$ from the sum of $$\displaystyle { 2b }^{ 2 }-2bc-{ c }^{ 2 }$$ and $$\displaystyle { c }^{ 2 }+2bc-{ b }^{ 2 }$$.

A
$$\displaystyle { 13b }^{ 2 }-5bc+{ 5c }^{ 2 }$$

B
$$\displaystyle { -10b }^{ 2 }-bc-{ 5c }^{ 2 }$$

C
$$\displaystyle { 10b }^{ 2 }+bc-{ 5c }^{ 2 }$$

D
$$\displaystyle { -10b }^{ 2 }-5bc-{ 5c }^{ 2 }$$

Solution

According to the question,
$$\displaystyle \left\{ \left( { 2b }^{ 2 }-2bc-{ c }^{ 2 } \right) +\left( { c }^{ 2 }+2bc-{ b }^{ 2 } \right) \right\} -\left\{ \left( { 9b }^{ 2 }+{ 3c }^{ 2 } \right) +\left( { 2b }^{ 2 }+bc + { 2c }^{ 2 } \right) \right\} $$
=$$\displaystyle \left\{ \left( { 2b }^{ 2 }-{ b }^{ 2 } \right) +\left( -2bc+2bc \right) +\left( { c }^{ 2 }-{ c }^{ 2 } \right) \right\} -\left\{ \left( { 9b }^{ 2 }+{ 2b }^{ 2 } \right) +\left( { 3c }^{ 2 }+{ 2c }^{ 2 } \right) +bc \right\} $$
$$\displaystyle =\left( { b }^{ 2 } \right) -\left( { 11b }^{ 2 }+{ 5c }^{ 2 }+bc \right) $$

$$\displaystyle ={ b }^{ 2 }-{ 11b }^{ 2 }-{ 5c }^{ 2 }-bc$$

$$\displaystyle =-{ 10b }^{ 2 }-bc-{ 5c }^{ 2 }$$.
Question 4
1 / -0

$$\displaystyle 4x-\left( -2y+5x \right) $$ is equal to

A
$$\displaystyle 9x-2y$$

B
$$\displaystyle 9x+2y$$

C
$$\displaystyle x+2y$$

D
$$\displaystyle -x+2y$$

Solution

Given, $$\displaystyle 4x-\left( -2y+5x \right) $$
$$\displaystyle =4x+2y-5x$$
$$\displaystyle =-x+2y$$
Hence simplified form is $$-x+2y$$
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

Given expression is: $$\displaystyle \left( { a }^{ 3 }-{ 2a }^{ 2 }+4a-5 \right) -\left( -{ a }^{ 3 }-8a+{ 2a }^{ 2 }+5 \right) $$
$$=\displaystyle { a }^{ 3 }-{ 2a }^{ 2 }+4a-5+{ a }^{ 3 }+8a-{ 2a }^{ 2 }-5$$
$$\displaystyle ={ 2a }^{ 3 }-{ 4a }^{ 2 }+12a-10$$
Hence simplified form of the given expression is $$={ 2a }^{ 3 }-{ 4a }^{ 2 }+12a-10$$
Question 6
1 / -0

If we take away $$\displaystyle -8abc$$ from $$\displaystyle -7abc$$, then the result is equal to

A
$$\displaystyle abc$$

B
$$\displaystyle 15abc$$

C
$$\displaystyle -abc$$

D
$$\displaystyle -15abc$$

Solution

We have to just subtract $$-8abc$$ from $$-7abc$$
$$=\displaystyle \left( -7abc \right) -\left( -8abc \right) $$
$$\displaystyle =-7abc+8abc$$
$$= abc$$
Question 7
1 / -0

What should be subtracted from $$\displaystyle { x }^{ 2 }-4xy-{ y }^{ 2 }$$ to get $$1$$?

A
$$\displaystyle { -x }^{ 2 }-4xy+{ y }^{ 2 }$$

B
$$\displaystyle { -x }^{ 2 }+4xy+{ y }^{ 2 }+1$$

C
$$\displaystyle { x }^{ 2 }-4xy-{ y }^{ 2 }-1$$

D
$$\displaystyle { -x }^{ 2 }+4xy+{ y }^{ 2 }-1$$

Solution

Let the algebraic expression that has to be subtracted be $$a$$. Then,
$$\displaystyle { x }^{ 2 }-4xy-{ y }^{ 2 }-a=1$$
$$\displaystyle a={ x }^{ 2 }-4xy-{ y }^{ 2 }-1$$
which required algebraic expression.
Question 8
1 / -0

What is the sum of $$\displaystyle \left( 4a+5b \right) ,\left( -6a+2b \right) ,\left( 7a-6b \right) $$?

A
$$\displaystyle -5a+b$$

B
$$\displaystyle 5a+b$$

C
$$\displaystyle 5a-b$$

D
$$\displaystyle -5a-b$$

Solution

We have to find sum of $$(4a+5b), (-6a+2b), (7a-6b)$$
$$\therefore$$ required sum $$=\displaystyle \left( 4a+5b \right) +\left( -6a+2b \right) +\left( 7a-6b \right) $$
$$\displaystyle =\left( 4a-6a+7a \right) +\left( 5b+2b-6b \right) $$
$$=\displaystyle 5a+b$$
Question 9
1 / -0

Simplify: $$(a^4-3a^2 + 6a - 8) - (a^4 - 10a + 4a^2 + 8)$$

A
$$-7a^2- 16a + 16$$

B
$$7a^2- 16a + 16$$

C
$$-7a^2 + 16a - 16$$

D
$$7a^2 + 16a - 16$$

Solution

$$(a^4-3a^2+6a-8)-(a^4-10a+4a^2+8)$$

$$=a^4-3a^2+6a-8-a^4+10a-4a^2-8$$

$$=a^4-a^4-3a^2-4a^2+6a+10a-8-8$$

$$=-7a^2+16a-16$$
Question 10
1 / -0

By how much is $$\displaystyle a^{4}+4a^{2}b^{2}+b^{4}$$ more than $$\displaystyle a^{4}-8a^{2}b^{2}+b^{4}$$ ?

A
$$\displaystyle 12a^{2}b^{2}$$

B
$$\displaystyle -12a^{2}b^{2}$$

C
$$\displaystyle 2a^{4}+2b^{4}$$

D
None

Solution

$$\displaystyle a^{4}+4a^{2}b^{2}+b^{4}$$
$$\displaystyle a^{4}-8a^{2}b^{2}+b^{4}$$
$$-$$ $$ + $$ $$-$$
$$\displaystyle \overline{\underline{12a^{2}b^{2}}}$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Algebraic Expressions Test - 10

Result

Algebraic Expressions Test - 10

Score

-

Rank

-

SHARING IS CARING

Question 1

$$\displaystyle 2p+2q$$

$$\displaystyle 2p$$

$$\displaystyle 2q$$

$$0$$

Solution

Question 2

$$\displaystyle { 2a }^{ 2 }$$

$$\displaystyle { a }^{ 2 }$$

0

$$\displaystyle { -2a }^{ 2 }$$

Solution

Question 3

$$\displaystyle { 13b }^{ 2 }-5bc+{ 5c }^{ 2 }$$

$$\displaystyle { -10b }^{ 2 }-bc-{ 5c }^{ 2 }$$

$$\displaystyle { 10b }^{ 2 }+bc-{ 5c }^{ 2 }$$

$$\displaystyle { -10b }^{ 2 }-5bc-{ 5c }^{ 2 }$$

Solution

Question 4

$$\displaystyle 9x-2y$$

$$\displaystyle 9x+2y$$

$$\displaystyle x+2y$$

$$\displaystyle -x+2y$$

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

$$\displaystyle abc$$

$$\displaystyle 15abc$$

$$\displaystyle -abc$$

$$\displaystyle -15abc$$

Solution

Question 7

$$\displaystyle { -x }^{ 2 }-4xy+{ y }^{ 2 }$$

$$\displaystyle { -x }^{ 2 }+4xy+{ y }^{ 2 }+1$$

$$\displaystyle { x }^{ 2 }-4xy-{ y }^{ 2 }-1$$

$$\displaystyle { -x }^{ 2 }+4xy+{ y }^{ 2 }-1$$

Solution

Question 8

$$\displaystyle -5a+b$$

$$\displaystyle 5a+b$$

$$\displaystyle 5a-b$$

$$\displaystyle -5a-b$$

Solution

Question 9

$$-7a^2- 16a + 16$$

$$7a^2- 16a + 16$$

$$-7a^2 + 16a - 16$$

$$7a^2 + 16a - 16$$

Solution

Question 10

$$\displaystyle 12a^{2}b^{2}$$

$$\displaystyle -12a^{2}b^{2}$$

$$\displaystyle 2a^{4}+2b^{4}$$

None

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.