Algebraic Expressions Test

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Algebraic Expressions Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

Add the following expressions $$2a+b+7$$ and $$4a+2b+3$$.

A
$$6a+2b+5$$

B
$$3b-6a+5$$

C
$$6ab+3b-10$$

D
$$6a+3b+10$$

Solution

Adding $$(2a+b+7)$$ and $$(4a+2b+3)$$,
$$2a+b+7$$
+$$4a+2b+3$$
___
$$6a+3b+10$$
Question 2
1 / -0

Which polynomial should be added to $$2x^4-3x^2+5x+8$$ to get $$2x^2-5x+4$$?

A
$$x^3+5x^2-x$$

B
$$2x^5+x^2-10x-9$$

C
$$-2x^4+5x^2-1$$

D
$$-2x^4+5x^2-10x-4$$

Solution

The sum of two polynomials=$$2x^2-5x+4$$
Let one polynomial be $$p$$.
Therefore,
$$2x^4-3x^2+5x+8 +p=2x^2-5x+4$$
$$=>p=2x^2-5x+4-2x^4+3x^2-5x-8$$
$$=>p=-2x^4+5x^2-10x-4$$
The polynomial to be added is $$-2x^4+5x^2-10x-4$$
Question 3
1 / -0

Simplify :
$$(3x^2-2x+1)+(x^2+5x-3)+(4x^2+8)$$

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

B
$$x^2+x$$

C
$$x^2+x_6$$

D
$$8x^2+x+9$$

Solution

$$(3x^2-2x+1)+(x^2+5x-3)+(4x^2+8)$$

$$=3x^2-2x+1+x^2+5x-3+4x^2+8$$

$$=8x^2+3x+6$$
Question 4
1 / -0

Subtract the second polynomial from the first :

$$x^4+x^2+x-1\, ; \, x^4-x^3-x^2+1$$

A
$$2x^2+x-2$$

B
$$x^3+2x^2+x-2$$

C
$$x^3+2x^2+x-2$$

D
$$x+2x^2-2$$

Solution

$$\begin{aligned}{}\left( {{x^4} + {x^2} + x - 1} \right) - \left( {{x^4} - {x^3} - {x^2} + 1} \right) &= {x^4} + {x^2} + x - 1 - {x^4} + {x^3} + {x^2} - 1\\ &= {x^4} - {x^4} + {x^3} + {x^2} + {x^2} + x - 1 - 1\\ &= {x^3} + 2{x^2} + x - 2\end{aligned}$$

Hence, option $$B$$ is correct.
Question 5
1 / -0

Add the given expressions $$5m+0.3n-1.2t; \, \, 0.23m - 2.8t + 4n$$

A
$$5.3m + 4.13n-4t$$

B
$$5.23m + 4.3n-4t$$

C
$$52.33m + 0.43n-4t$$

D
$$5.23m + 43n-4t$$

Solution

$$5m+0.3n-1.2t+ 0.23m-2.8t+4n$$
$$=5m+0.3n-1.2t+0.23m+4n-2.8t$$
$$=5.23m + 4.3n-4t$$
Question 6
1 / -0

Evaluate : $$ 7x-9y+3-3x-5y+8 $$

A
$$4x+4y+11 $$

B
$$4x-14y+11 $$

C
Cannot be determined

D
None of these

Solution

$$\quad We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (7-3)x+(-9-5)y+(3+8)=4x-14y+11$$
Question 7
1 / -0

What should be added to $$6x^2-3xy+4y^2$$ to get $$2y^2+xy-4x^2$$?

A
$$-x^2-y^2+4y$$

B
$$-10x^2-y^2+4xy$$

C
$$x^2-2y^2+4x$$

D
$$-10x^2-2y^2+4xy$$

Solution

Let the required expression be $$P$$
$$P=(2y^{ 2 }+xy-4x^{ 2 })-(6x^{ 2 }-3xy+4y^{ 2 })$$
$$=-4x^{ 2 }+2y^{ 2 }+xy-6x^{ 2 }+3xy-4y^{ 2 }$$
$$=-10x^2-2y^2+4xy$$
Question 8
1 / -0

Subtract $$6x+8y+4$$ from the sum of $$4x-2y+3$$ and $$2y-x+3$$?

A
$$-x-8y-2$$

B
$$-3x-8y+2$$

C
$$-3x-y+1$$

D
$$-x-8y+2$$

Solution

Consider, $$(4x-2y+3)+(2y-x+3)$$
$$=4x-2y+3+2y-x+3$$
$$=3x+6$$

Subtracting $$6x+8y+4$$ from $$3x+6$$ we get,
$$(3x+6)-(6x+8y+4)$$
$$=3x+6-6x-8y+4$$
$$=-3x-8y+2$$
Question 9
1 / -0

Add: $$2x+y+z$$ ; $$-x+2y+2z$$ and $$x-y-z$$

A
$$2x+2y+2z$$

B
$$3x+5y+z$$

C
$$3x-3y-z$$

D
None of these

Solution

Sum of $$(2x+y+z),$$ $$(-x+2y+2z)$$ and $$(x-y-z)$$ is:

$$=\displaystyle \left( 2x+y+z \right) +\left( -x+2y+2z \right) +\left( x-y-z \right) $$

$$=(2x-x+x)+(y+2y-y)+(z+2z-z) $$

$$=2x+2y+2z$$

$$=2(x+y+z)$$
Question 10
1 / -0

The sum of $$\displaystyle 3ab, -8ab$$ and $$5ab$$ is equal to

A
$$\displaystyle 10ab$$

B
$$\displaystyle 16ab$$

C
$$\displaystyle ab$$

D
$$0$$

Solution

We have to find sum of $$3ab, -8ab, 5ab$$

$$\therefore$$ required sum is $$=\displaystyle 3ab+\left( -8ab \right) +5ab$$

$$\displaystyle =8ab-8ab=0$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions Test - 9

Result

Algebraic Expressions Test - 9

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SHARING IS CARING

Question 1

$$6a+2b+5$$

$$3b-6a+5$$

$$6ab+3b-10$$

$$6a+3b+10$$

Solution

Question 2

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

$$2x^5+x^2-10x-9$$

$$-2x^4+5x^2-1$$

$$-2x^4+5x^2-10x-4$$

Solution

Question 3

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

$$x^2+x$$

$$x^2+x_6$$

$$8x^2+x+9$$

Solution

Question 4

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

$$x^3+2x^2+x-2$$

$$x^3+2x^2+x-2$$

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

Solution

Question 5

$$5.3m + 4.13n-4t$$

$$5.23m + 4.3n-4t$$

$$52.33m + 0.43n-4t$$

$$5.23m + 43n-4t$$

Solution

Question 6

$$4x+4y+11 $$

$$4x-14y+11 $$

Cannot be determined

None of these

Solution

Question 7

$$-x^2-y^2+4y$$

$$-10x^2-y^2+4xy$$

$$x^2-2y^2+4x$$

$$-10x^2-2y^2+4xy$$

Solution

Question 8

$$-x-8y-2$$

$$-3x-8y+2$$

$$-3x-y+1$$

$$-x-8y+2$$

Solution

Question 9

$$2x+2y+2z$$

$$3x+5y+z$$

$$3x-3y-z$$

None of these

Solution

Question 10

$$\displaystyle 10ab$$

$$\displaystyle 16ab$$

$$\displaystyle ab$$

$$0$$

Solution

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