Algebraic Expressions Test

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Algebraic Expressions Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

If $$P=3x-4y-8z$$, $$Q=-10y+7x+11z$$ and $$R=19z-6y+4x$$, then $$P-Q+R$$ is equal to

A
$$13x-20y+16z$$

B
$$0$$

C
$$x+y+z$$

D
$$2x-4y+3z$$

Solution

$$P=3x-4y-8z$$
$$Q=-10y+7x+11z$$
$$R=19z-6y+4x$$
$$\therefore P-Q+R=(3x-4y-8z)-(-10y+7x+11z)+(19z-6y+4x)$$
$$=3x-4y-8z+10y-7x-11z+19z-6y+4x$$
$$=3x-7x+4x-4y+10y-6y-8z-11z+19z=7x-7x-10y+10y-19z+19z=0$$
Question 2
1 / -0

What is the simplified result of following the steps in order?
$$(1)$$ add $$5y$$ to $$2x$$
$$(2)$$ multiply the sum by $$3$$
$$(3)$$ subtract x$$+$$y from the product

A
$$5x+14y$$

B
$$5x+16y$$

C
$$5x+5y$$

D
$$6x+4y$$

E
$$3x+12y$$

Solution
Question 3
1 / -0

The sum of three expressions is $${ x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }$$. If two of them are $$4{ x }^{ 2 }-5{ y }^{ 2 }+3{ z }^{ 2 }$$ and $$-3{ x }^{ 2 }+4{ y }^{ 2 }+2{ z }^{ 2 }$$, the third expression is

A
$$2{ x }^{ 2 }+2{ z }^{ 2 }$$

B
$$2{ y }^{ 2 }$$

C
$$2{ x }^{ 2 }+2{ y }^{ 2 }-{ z }^{ 2 }$$

D
$$2{ y }^{ 2 }-4{ z }^{ 2 }$$

Solution

Add two expressions

$$\Rightarrow \left ( 4x^{2}-5y^{2}+3z^{2} \right )+(-3x^{2}+4y^{2}+2z^{2})$$

$$=\left ( 4x^{2}-5y^{2}+3z^{2}-3x^{2}+4y^{2}+2z^{2} \right )$$

$$=4x^{2}-3x^{2}-5y^{2}+4y^{2}+3z^{2}+2z^{2}$$

$$=x^{2}-y^{2}+5z^{2}$$

But $$x^{2}-y^{2}+5z^{2}+P(x)=x^{2}+y^{2}+z^{2}$$, where $$P(x)$$ is the third expression

$$\therefore P(x)=\left ( x^{2}+y^{2}+z^{2} \right )-\left ( x^{2}-y^{2}+5z^{2} \right )$$

$$=x^{2}+y^{2}+z^{2}-x^{2}+y^{2}-5z^{2}=2y^{2}-4z^{2}$$
Question 4
1 / -0

$$\left( 4p{ x }^{ 2 }+5{ q }^{ 2 }y-9rz \right) -\left( -3{ q }^{ 2 }y+7p{ x }^{ 2 }-rz \right) =$$

A
$$11p{ x }^{ 2 }+9{ q }^{ 2 }y-10rz$$

B
$$-3p{ x }^{ 2 }+8q^{2}y-8rz$$

C
$$11p{ x }^{ 2 }+8{ q }^{ 2 }y-8rz$$

D
$$-3p{ x }^{ 2 }-8{ q }^{ 2 }y-10rz$$

Solution

$$(4px^{2}+5q^{2}y-9rz)-(-3q^{2}y+7px^{2}-rz)$$
$$=4px^{2}+5q^{2}y-9rz+3q^{2}y-7px^{2}+rz$$
$$=4px^{2}-7px^{2}+5q^{2}y+3q^{2}y-9rz+rz$$
$$=-3px^{2}+8q^{2}y-8rz$$
Question 5
1 / -0

The sum of three expressions is $$x^{2}+y^{2}+z^{2}.$$ If two of them are $$4x^{2}-5y^{2}+z^{2}$$ and $$-3x^{2}+4y^{2}+2z^{2}$$, find the third expression.

A
$$2x^{2}+2z^{2}$$

B
$$2y^{2}$$

C
$$2x^{2}+2y^{2}-z^{2}$$

D
$$2y^{2}-2z^{2}$$

Solution

Let the third expression be $$a$$ then,
$$ a+(4x^{2}-5y^{2}+z^{2})+(-3x^{2}+4y^{2}+2z^{2}) = x^{2}+y^{2}+z^{2}$$
$$ \Rightarrow a+(x^{2}-y^{2}+3z^{2})=(x^{2}+y^{2}+z^{2})$$
$$ \Rightarrow a = (x^{2}+y^{2}+z^{2})-x^{2}+y^{2}-3z^{2}$$
$$ \Rightarrow a = 2y^{2}-2z^{2}$$

Hence, option $$D$$ is correct.
Question 6
1 / -0

Subtract $$2x^{3}-4x^{2}+3x+5$$ from $$4x^{2}+x^{2}+x+6$$, then the resultant value is

A
$$6x^{3}+5x^{2}-2x+1$$

B
$$2x^{3}+5x^{2}-2x+1$$

C
$$2x^{3}-5x^{2}-2x+1$$

D
$$2x^{3}-5x^{2}+2x-1$$

Solution
Question 7
1 / -0

Add: $$2u+3v,\,\,-2v+3w,\,\,3u-v+2w$$

A
$$5u-5w$$

B
$$5u+5w$$

C
$$u-w$$

D
$$u+w$$

Solution

given, $$\left(2u+3v+3u-v+2w\right)+\left(-2v+3w\right)$$

$$=5u+2v+2w-2v+3w$$

$$=5u+5w$$
Question 8
1 / -0

Simplify: $$a-[b-\{c-(a-b-c)\}-c]+a$$

A
$$a-2c$$

B
$$a-3c$$

C
$$a+3c$$

D
$$a+2c$$

Solution
Question 9
1 / -0

The sum of $$(6a+4b-c+3), (2b-3c+4), (11b-7a+2c-1)$$ and $$(2c-5a-6)$$ is

A
$$(4a-6b+2)$$

B
$$(-3a+14b-3c+2)$$

C
$$(-6a+17b)$$

D
$$(-6a+6b+c-4)$$

Solution

$$(6a+4b−c+3)+(2b−3c+4)+(11b−7a+2c−1)+(2c−5a−6)$$

$$\Rightarrow$$ $$6a+4b−c+3+2b−3c+4+11b−7a+2c−1+2c−5a−6$$

Now arranging and combining the like terms,

$$\Rightarrow$$ $$(6a-7a-5a)+(4b+2b+11b)+(-c-3c+2c+2c)+(3+4-1-6)$$

$$\Rightarrow$$ $$-6a+17b$$

$$\therefore$$ The sum of $$(6a+4b−c+3),(2b−3c+4),(11b−7a+2c−1)$$ and $$(2c−5a−6)$$ is $$(-6a+17b)$$
Question 10
1 / -0

The sum of $${x}^{4}-xy+2{y}^{2}$$ and $$-{x}^{4}+xy+2{y}^{2}$$ is

A
Monomial and polynomial in $$y$$

B
Binomial and Polynomial

C
Trinomial and polynomial

D
Monomial and polynomial in $$x$$

Solution

Required sum $$={x}^{4}-xy+2{y}^{2}+-{x}^{4}+xy+2{y}^{2}$$
$$={x}^{4}-xy+2{y}^{2}-{x}^{4}+xy+2{y}^{2}$$
$$=[{x}^{4}+)-{x}^{4})]+(-xy+xy)+(2{y}^{2}+2{y}^{2})$$
$$=0+0+4{y}^{2}=4{y}^{2}$$
$$4{y}^{2}$$ is a monomial and polynomial in $$y$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions Test - 17

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Algebraic Expressions Test - 17

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SHARING IS CARING

Question 1

$$13x-20y+16z$$

$$0$$

$$x+y+z$$

$$2x-4y+3z$$

Solution

Question 2

$$5x+14y$$

$$5x+16y$$

$$5x+5y$$

$$6x+4y$$

$$3x+12y$$

Solution

Question 3

$$2{ x }^{ 2 }+2{ z }^{ 2 }$$

$$2{ y }^{ 2 }$$

$$2{ x }^{ 2 }+2{ y }^{ 2 }-{ z }^{ 2 }$$

$$2{ y }^{ 2 }-4{ z }^{ 2 }$$

Solution

Question 4

$$11p{ x }^{ 2 }+9{ q }^{ 2 }y-10rz$$

$$-3p{ x }^{ 2 }+8q^{2}y-8rz$$

$$11p{ x }^{ 2 }+8{ q }^{ 2 }y-8rz$$

$$-3p{ x }^{ 2 }-8{ q }^{ 2 }y-10rz$$

Solution

Question 5

$$2x^{2}+2z^{2}$$

$$2y^{2}$$

$$2x^{2}+2y^{2}-z^{2}$$

$$2y^{2}-2z^{2}$$

Solution

Question 6

$$6x^{3}+5x^{2}-2x+1$$

$$2x^{3}+5x^{2}-2x+1$$

$$2x^{3}-5x^{2}-2x+1$$

$$2x^{3}-5x^{2}+2x-1$$

Solution

Question 7

$$5u-5w$$

$$5u+5w$$

$$u-w$$

$$u+w$$

Solution

Question 8

$$a-2c$$

$$a-3c$$

$$a+3c$$

$$a+2c$$

Solution

Question 9

$$(4a-6b+2)$$

$$(-3a+14b-3c+2)$$

$$(-6a+17b)$$

$$(-6a+6b+c-4)$$

Solution

Question 10

Monomial and polynomial in $$y$$

Binomial and Polynomial

Trinomial and polynomial

Monomial and polynomial in $$x$$

Solution

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