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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Algebraic Expressions Test - 17

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Question 1

13x−20y+16z13x-20y+16z13x−20y+16z

000

x+y+zx+y+zx+y+z

2x−4y+3z2x-4y+3z2x−4y+3z

Solution

Question 2

5x+14y5x+14y5x+14y

5x+16y5x+16y5x+16y

5x+5y5x+5y5x+5y

6x+4y6x+4y6x+4y

3x+12y3x+12y3x+12y

Solution

Question 3

2x2+2z22{ x }^{ 2 }+2{ z }^{ 2 }2x2+2z2

2y22{ y }^{ 2 }2y2

2x2+2y2−z22{ x }^{ 2 }+2{ y }^{ 2 }-{ z }^{ 2 }2x2+2y2−z2

2y2−4z22{ y }^{ 2 }-4{ z }^{ 2 }2y2−4z2

Solution

Question 4

11px2+9q2y−10rz11p{ x }^{ 2 }+9{ q }^{ 2 }y-10rz11px2+9q2y−10rz

−3px2+8q2y−8rz-3p{ x }^{ 2 }+8q^{2}y-8rz−3px2+8q2y−8rz

11px2+8q2y−8rz11p{ x }^{ 2 }+8{ q }^{ 2 }y-8rz11px2+8q2y−8rz

−3px2−8q2y−10rz-3p{ x }^{ 2 }-8{ q }^{ 2 }y-10rz−3px2−8q2y−10rz

Solution

Question 5

2x2+2z22x^{2}+2z^{2}2x2+2z2

2y22y^{2}2y2

2x2+2y2−z22x^{2}+2y^{2}-z^{2}2x2+2y2−z2

2y2−2z22y^{2}-2z^{2}2y2−2z2

Solution

Question 6

6x3+5x2−2x+16x^{3}+5x^{2}-2x+16x3+5x2−2x+1

2x3+5x2−2x+12x^{3}+5x^{2}-2x+12x3+5x2−2x+1

2x3−5x2−2x+12x^{3}-5x^{2}-2x+12x3−5x2−2x+1

2x3−5x2+2x−12x^{3}-5x^{2}+2x-12x3−5x2+2x−1

Solution

Question 7

5u−5w5u-5w5u−5w

5u+5w5u+5w5u+5w

u−wu-wu−w

u+wu+wu+w

Solution

Question 8

a−2ca-2ca−2c

a−3ca-3ca−3c

a+3ca+3ca+3c

a+2ca+2ca+2c

Solution

Question 9

(4a−6b+2)(4a-6b+2)(4a−6b+2)

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

(−6a+17b)(-6a+17b)(−6a+17b)

(−6a+6b+c−4)(-6a+6b+c-4)(−6a+6b+c−4)

Solution

Question 10

Monomial and polynomial in yyy

Binomial and Polynomial

Trinomial and polynomial

Monomial and polynomial in xxx

Solution

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$13x-20y+16z$

$0$

$x+y+z$

$2x-4y+3z$

$5x+14y$

$5x+16y$

$5x+5y$

$6x+4y$

$3x+12y$

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

$2{ y }^{ 2 }$

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

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

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

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

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

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

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

$2y^{2}$

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

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

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

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

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

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

$5u-5w$

$5u+5w$

$u-w$

$u+w$

$a-2c$

$a-3c$

$a+3c$

$a+2c$

$(4a-6b+2)$

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

$(-6a+17b)$

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

Monomial and polynomial in $y$

Monomial and polynomial in $x$