Algebraic Expressions Test

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Algebraic Expressions Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$4a^{2}b^{2}$$

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

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

D
$$10a^{2}b^{2}$$

Solution

We have two expressions
$$a^{4}-4a^{2}b^{2}+b^{2}$$ ............(1)
$$a^{4}-8a^{2}b^{2}+b^{2}$$ ............(2)
Subtract (2) from (1), we get
$$a^{4}-4a^{2}b^{2}+b^{2} - (a^{4}-8a^{2}b^{2}+b^{4})$$
$$= a^{4}-4a^{2}b^{2}+b^{2} - a^{4}+8a^{2}b^{2}-b^{4}$$
$$= -4a^{2}+8a^{2}b^{2}$$
$$= 4a^{2}b^{2}$$
Question 2
1 / -0

The sum of $$3x+4y-5z,\ 5y+2x,\ 7x-8y$$ and $$4x-9y-5z$$ is

A
$$16x-8y-10z$$

B
$$8x-16y-5z$$

C
$$116x+8y+10z$$

D
None of these

Solution

Adding the given terms:
$$ (3x+4y-5z)+(5y+2x)+(7x-8y)+(4x-9y-5z) $$$$=x(3+2+7+4)+y(4+5-8-9)+z(-5-5)$$
$$ = 16x-8y-10z $$
Hence, Option A is correct.
Question 3
1 / -0

Simplify combining like terms :
$$p-(p-q)-q-(q-p)$$

A
$$q-p$$

B
$$q$$

C
$$0$$

D
$$p-q$$

Solution

$$p-(p-q)-q-(q-p)$$
$$=p-p+q-q-q+p$$
$$=p-q$$
Question 4
1 / -0

add $$2x$$ and $$3x$$:-

A
$$9x$$

B
$$3x$$

C
$$5x$$

D
$$7x$$

Solution

$$2x+3x=(2+3)x=5x$$
Question 5
1 / -0

What must be added to $$5x^{3}-2x^{2}+6x+7$$ to make the sum $$x^{3}+3x^{2}-x+1$$?

A
$$4x^{3}-5x^{2}+7x+6$$

B
$$4x^{3}+5x^{2}-7x+6$$

C
$$-4x^{3}+5x^{2}-7x-6$$

D
$$None\ of\ these$$

Solution

$$\left( {x}^{3} + 3 {x}^{2} - x + 1 \right) - \left( 5 {x}^{3} - 2 {x}^{2} + 6x + 7 \right)$$
$$= \left( 1 - 5 \right) {x}^{3} + \left( 3 + 2 \right) {x}^{2} - \left( 1 + 6 \right) x + 1 - 7$$
$$= -4 {x}^{3} + 5 {x}^{2} - 7x - 6$$
Hence $$\left( -4 {x}^{3} + 5 {x}^{2} - 7x - 6 \right)$$ must be added to $$\left( {x}^{3} + 3 {x}^{2} - x + 1 \right)$$ to make the sum $$\left( 5 {x}^{3} - 2 {x}^{2} + 6x + 7 \right)$$.
Question 6
1 / -0

What must be added to $${ 7z }^{ 3 }-{ 11z }^{ 2 }-129$$ to get $${ 5z }^{ 2 }+7z-92$$ ?

A
$${ 7z }^{ 3 }+{ 16z }^{ 2 }+7z+37$$

B
$$-{ 7z }^{ 3 }+{ 16z }^{ 2 }+7z+37$$

C
$$-{ 7z }^{ 3 }+{ 16z }^{ 2 }+7z-37$$

D
$$-{ 7z }^{ 3 }-{ 7z }^{ 2 }+7z-37$$

Solution

Let a must be added.
Then,
$$7z^3 - 11z^2 -129 + a = 5z^2 +7z -92$$
$$\rightarrow a = -7z^3 + 16z^2 + 7z + 37$$

Thus, B is the correct answer.
Question 7
1 / -0

From the sum of $$z^3+3z^2+5z+8$$ and $$4z^3+2z^2-7z-2$$ subtract $$2z^3-3z^2+z-4$$.

A
$$0$$

B
$$8z^2-3z$$

C
$$3z^3+8z^2-3z+10$$

D
$$2-z$$

Solution

The sum of $$z^3+3z^2+5z+8$$ and $$4z^3+2z^2-7z-2$$ is,

$$=z^3+3z^2+5z+8 + 4z^3+2z^2-7z-2$$

$$=5z^3+5z^2-2z+6$$

Now,

Subtracting $$2z^3-3z^2+z-4$$ from $$5z^3+5z^2-2z+6$$ we get,

$$5z^3+5z^2-2z+6$$ $$-(2z^3-3z^2+z-4)$$ $$=5z^3+5z^2-2z+6$$ $$-2z^3+3z^2-z+4$$

$$=3z^3+8z^2-3z+10$$
Question 8
1 / -0

Subtract the second expression from the first:
$$5x^2-6xy+2$$ and $$3x^2+10xy-8$$.

A
$$x^2-16xy-10$$

B
$$2x^2+86xy+10$$

C
$$x^2-8xy- 50$$

D
$$2x^2-16xy+10$$

Solution

$$(5x^2-6xy+2) - (3x^2+10xy-8)$$
$$=5x^2-6xy+2-3x^2-10xy+8$$
$$=2x^2-16xy+10$$
Question 9
1 / -0

Simplify: $$\displaystyle { 2x }^{ 2 }y-{ 3xy }^{ 2 }+{ 2x }^{ 2 }y-{ 4x }^{ 2 }y+{ 2xy }^{ 2 }$$

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

B
$$\displaystyle { 2x }^{ 2 }y-8xy$$

C
$$-xy^2$$

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

Solution

$$\displaystyle { 2x }^{ 2 }y-{ 3xy }^{ 2 }+{ 2x }^{ 2 }y-{ 4x }^{ 2 }y+{ 2xy }^{ 2 }$$
$$\displaystyle =\left( { 2x }^{ 2 }y+{ 2x }^{ 2 }y-{ 4x }^{ 2 }y \right) +\left( -{ 3xy }^{ 2 }+{ 2xy }^{ 2 } \right) , $$ (Arranging like terms together)
$$\displaystyle =0-{ xy }^{ 2 }=-{ xy }^{ 2 }$$
Hence simplified form of the given expression is $$-xy^2$$
Question 10
1 / -0

Subtract $$4a -7ab + 3b + 12$$ from $$12a- 9ab + 5b- 3$$.

A
$$8a+2ab + 2b+15$$

B
$$8a + 2b+15$$

C
$$8a-2ab + 2b+15$$

D
$$8a-2ab + 2b-15$$

Solution

subtract $$4a - 7ab + 3b + 12$$ from $$12a- 9ab + 5b - 3$$

$$=12a- 9ab + 5b - 3-(4a - 7ab + 3b+12)$$

$$=12a- 9ab + 5b - 3-4a +7ab - 3b-12$$

$$=8a-2ab+2b-15$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions Test - 13

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Algebraic Expressions Test - 13

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SHARING IS CARING

Question 1

$$4a^{2}b^{2}$$

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

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

$$10a^{2}b^{2}$$

Solution

Question 2

$$16x-8y-10z$$

$$8x-16y-5z$$

$$116x+8y+10z$$

None of these

Solution

Question 3

$$q-p$$

$$q$$

$$0$$

$$p-q$$

Solution

Question 4

$$9x$$

$$3x$$

$$5x$$

$$7x$$

Solution

Question 5

$$4x^{3}-5x^{2}+7x+6$$

$$4x^{3}+5x^{2}-7x+6$$

$$-4x^{3}+5x^{2}-7x-6$$

$$None\ of\ these$$

Solution

Question 6

$${ 7z }^{ 3 }+{ 16z }^{ 2 }+7z+37$$

$$-{ 7z }^{ 3 }+{ 16z }^{ 2 }+7z+37$$

$$-{ 7z }^{ 3 }+{ 16z }^{ 2 }+7z-37$$

$$-{ 7z }^{ 3 }-{ 7z }^{ 2 }+7z-37$$

Solution

Question 7

$$0$$

$$8z^2-3z$$

$$3z^3+8z^2-3z+10$$

$$2-z$$

Solution

Question 8

$$x^2-16xy-10$$

$$2x^2+86xy+10$$

$$x^2-8xy- 50$$

$$2x^2-16xy+10$$

Solution

Question 9

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

$$\displaystyle { 2x }^{ 2 }y-8xy$$

$$-xy^2$$

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

Solution

Question 10

$$8a+2ab + 2b+15$$

$$8a + 2b+15$$

$$8a-2ab + 2b+15$$

$$8a-2ab + 2b-15$$

Solution

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