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CBSE Questions for Class 7 Maths Algebraic Expressions Quiz 3 - MCQExams.com
CBSE
Class 7 Maths
Algebraic Expressions
Quiz 3
$$\displaystyle 5a-\{ { 3a-(4-a)-4\} }$$ is equal to
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$$\displaystyle 3a+8$$
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$$\displaystyle a-8$$
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$$\displaystyle a+8$$
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$$\displaystyle 3a-8$$
Explanation
Given, $$\displaystyle 5a-\{ { 3a-(4-a)-4\} }$$
$$=\displaystyle 5a-\left\{ 3a-4+a-4 \right\} $$
$$=\displaystyle 5a-\left\{ 4a-8 \right\} $$
$$\displaystyle= 5a-4a+8$$
$$=\displaystyle a+8$$, which is simplified form.
$$\displaystyle { a }^{ 2 }-\left( -{ a }^{ 2 } \right) $$ is equal to
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$$\displaystyle { 2a }^{ 2 }$$
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$$\displaystyle { a }^{ 2 }$$
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0
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$$\displaystyle { -2a }^{ 2 }$$
Explanation
Given, $$\displaystyle { a }^{ 2 }-\left( { -a }^{ 2 } \right) ={ a }^{ 2 }+{ a }^{ 2 }=2a^2$$.
Hence simplified form of the given expression is $$2a^2$$.
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 $$\displaystyle { c }^{ 2 }+2bc-{ b }^{ 2 }$$.
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$$\displaystyle { 13b }^{ 2 }-5bc+{ 5c }^{ 2 }$$
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$$\displaystyle { -10b }^{ 2 }-bc-{ 5c }^{ 2 }$$
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$$\displaystyle { 10b }^{ 2 }+bc-{ 5c }^{ 2 }$$
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$$\displaystyle { -10b }^{ 2 }-5bc-{ 5c }^{ 2 }$$
Explanation
According to the question,
$$\displaystyle \left\{ \left( { 2b }^{ 2 }-2bc-{ c }^{ 2 } \right) +\left( { c }^{ 2 }+2bc-{ b }^{ 2 } \right) \right\} -\left\{ \left( { 9b }^{ 2 }+{ 3c }^{ 2 } \right) +\left( { 2b }^{ 2 }+bc + { 2c }^{ 2 } \right) \right\} $$
=$$\displaystyle \left\{ \left( { 2b }^{ 2 }-{ b }^{ 2 } \right) +\left( -2bc+2bc \right) +\left( { c }^{ 2 }-{ c }^{ 2 } \right) \right\} -\left\{ \left( { 9b }^{ 2 }+{ 2b }^{ 2 } \right) +\left( { 3c }^{ 2 }+{ 2c }^{ 2 } \right) +bc \right\} $$
$$\displaystyle =\left( { b }^{ 2 } \right) -\left( { 11b }^{ 2 }+{ 5c }^{ 2 }+bc \right) $$
$$\displaystyle ={ b }^{ 2 }-{ 11b }^{ 2 }-{ 5c }^{ 2 }-bc$$
$$\displaystyle =-{ 10b }^{ 2 }-bc-{ 5c }^{ 2 }$$.
Simplify: $$\displaystyle \left( { a }^{ 3 }-{ 2a }^{ 2 }+4a-5 \right) -\left( -{ a }^{ 3 }-8a+{ 2a }^{ 2 }+5 \right) $$
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$$\displaystyle { 2a }^{ 3 }+{ 7a }^{ 2 }+6a-10$$
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$$\displaystyle { 2a }^{ 3 }+{ 7a }^{ 2 }+12a-10$$
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$$\displaystyle { 2a }^{ 3 }-{ 4a }^{ 2 }+12a-10$$
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$$\displaystyle { 2a }^{ 3 }-{ 4a }^{ 2 }+6a-10$$
Explanation
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 $$={ 2a }^{ 3 }-{ 4a }^{ 2 }+12a-10$$
Add the following:
$$ab-bc,bc-ca,ca -ab$$
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0
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1
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2
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-1
Explanation
Adding them
$$=ad-bc+bc-ca+ca-ab$$
$$=0$$
What should be subtracted from $$\displaystyle { x }^{ 2 }-4xy-{ y }^{ 2 }$$ to get $$1$$?
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$$\displaystyle { -x }^{ 2 }-4xy+{ y }^{ 2 }$$
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$$\displaystyle { -x }^{ 2 }+4xy+{ y }^{ 2 }+1$$
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$$\displaystyle { x }^{ 2 }-4xy-{ y }^{ 2 }-1$$
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$$\displaystyle { -x }^{ 2 }+4xy+{ y }^{ 2 }-1$$
Explanation
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.
Simplify: $$(a^4-3a^2 + 6a - 8) - (a^4 - 10a + 4a^2 + 8)$$
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$$-7a^2- 16a + 16$$
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$$7a^2- 16a + 16$$
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$$-7a^2 + 16a - 16$$
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$$7a^2 + 16a - 16$$
Explanation
$$(a^4-3a^2+6a-8)-(a^4-10a+4a^2+8)$$
$$=a^4-3a^2+6a-8-a^4+10a-4a^2-8$$
$$=a^4-a^4-3a^2-4a^2+6a+10a-8-8$$
$$=-7a^2+16a-16$$
Add the following:
$$3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c$$
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$$6a-7b-3c$$
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$$6a-7b+3c$$
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$$6a+7b-3c$$
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$$5a-7b-3c$$
Explanation
After adding we get:
$$(3a - 4b + 4c) + (2a + 3b - 8c) +( a - 6b + c)$$
$$=3a + 2a+ a- 4b + 3b- 6b+ 4c- 8c + c$$
$$=6a - 7b - 3c$$
Subtract
$$3a^2b $$ from $$-5a^2b$$
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$$-2a^2b$$
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$$2a^2b$$
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$$-8a^2b$$
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$$0$$
Explanation
After Subtracting $$3a^2b $$ from $$-5a^2b$$ we get,
$$=-5a^2b-3a^2b$$
$$=-8a^2b$$
By how much is x$$^4$$ + 4x$$^2$$y$$^2$$ + y$$^4$$ more than x$$^4$$ - 8x$$^2$$y$$^2$$ + y$$^4$$ ?
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-12x$$^2$$y$$^2$$
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12x$$^2$$y$$^2$$
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2x$$^4$$ + 2y$$^4$$
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None of these
Explanation
(x
4
+ 4x
2
y
2
+ y
4
) - (x
4
- 8x
2
y
2
+ y
4
)
= x
4
+ 4x
2
y
2
+ y
4
- x
4
+ 8x
2
y
2
- y
4
= 12 x
2
y
2
What must be added to $$(x^3 + 3x - 8)$$ to get $$(3x^3 + x^2 + 6)$$?
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$$2x^3+x^2-3x+14$$
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$$2x^2+x^2+14$$
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$$2x^3+x^2-6x-14$$
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None of these
Explanation
Let, $$Y$$ is added to $$(x^3 + 3x - 8)$$ to get $$(3x^3 + x^2 + 6)$$
So,
$$(x^3 + 3x - 8) +Y= 3x^3 + x^2 + 6$$
$$\Rightarrow Y=(3x^3 + x^2 + 6) -(x^3 + 3x - 8)$$
$$\Rightarrow Y=3x^3 + x^2 + 6 -x^3 - 3x + 8$$
$$\Rightarrow Y=2x^3+x^2-3x+14$$
So, option $$A$$ is correct.
If we add two monomials, what will be the result?
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Monomial
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Binomial
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Polynomial
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Either $$A$$ or $$B$$
Explanation
If two monomials are added we will get a result which is addition of two terms.
So in most of the cases, the result will be a binomial but in other cases, when both terms differ by coefficients, their addition will give another monomial.
For eg. $$3x$$, $$4y$$ when added, gives $$3x+4y$$.
However, $$5x^2+7x^2$$ when added, gives $$5x^2+7x^2=12x^2$$.
Add the following:
$$5x - 8y + 2z, 3z - 4y - 2x,6y - z - x$$
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$$2x-6y-4z$$
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$$2x-6y+4z$$
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$$2x+6y+4z$$
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$$-2x-6y+4z$$
Explanation
After adding we get:
$$(5x - 8y + 2z)+ (3z - 4y - 2x)+(6y - z - x)$$
$$=5x- 2x - x- 8y- 4y+6y + 2z+ 3z- z$$
$$=2x - 6y + 4z$$
How many terms are there in the algebraic expression $$7x^3+2xy+z-7y$$?
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$$3$$
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$$4$$
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$$5$$
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$$6$$
Explanation
There are 4 terms.
The terms are $$7x^3, 2xy, z, 7y$$
Simplify the expression $$(2b^3c^2+b^2c-4bc)-(b^3c^2-b^2c-4bc)$$.
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0
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$$b^3c^2$$
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$$b^3c^2+2b^2c$$
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$$b^3c^2+2b^2c-8bc$$
Explanation
On simplification, we get
$$(2b^3c^2+b^2c-4bc)-(b^3c^2-b^2c-4bc)$$
$$\Rightarrow 2b^3c^2+b^2c-4bc-b^3c^2+b^2c+4bc$$
$$\Rightarrow b^3c^2+2b^2c$$
If two unlike terms are added , the result will be a
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monomial
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binomial
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trinomial
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polynomial
Explanation
Addition of two unlike terms will result in binomial.
Simplify $$(2x^2+4x+8)-(2x^2-4x+7)$$
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$$4x^2+8x+15$$
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$$2x^2+x+1$$
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$$8x+1$$
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$$8x+15$$
Explanation
On simplifying, we get
$$ (2x^2+4x+8)-(2x^2-4x+7)$$
$$\Rightarrow 2x^2+4x+8-2x^2+4x-7$$
$$\Rightarrow 8x+1$$
Subtract
$$\left( j{ k }^{ 2 }+2{ j }^{ 2 }k+5{ j }^{ 2 } \right) $$ from
$$\displaystyle \left( 5j{ k }^{ 2 }+5{ j }^{ 2 }-2{ j }^{ 2 }k \right) $$.
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$$\displaystyle -(4k{ j }^{ 2 }-4jk^2)$$
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$$\displaystyle 4j{ k }^{ 2 }-4{ j }^{ 2 }k$$
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$$\displaystyle 5{ j }^{ 2 }{ k }^{ 4 }-10{ j }^{ 4 }k$$
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$$\displaystyle 8{ j }^{ 2 }{ k }^{ 3 }+7{ j }^{ 2 }k-5{ j }^{ 2 }$$
Explanation
$$(5jk^2 + 5j^2 - 2j^2k) - (jk^2 + 2j^2k + 5j^2)$$
$$= (5jk^2 - jk^2) + (5j^2 - 5j^2) + (-2j^2k - 2j^2k)$$
$$= 4jk^2 - 4j^2k=-(4j^2k-4k^2j)$$
$$5x^{3} + 5x^{2} + 4x + 3 + 4x^{2} + 5x =$$
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$$9x^{3} + 4x^{2} + 4x + 5$$
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$$5x^{3} + 5x^{2} + 9x + 4$$
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$$5x^{3} + 9x^{2} + 9x + 3$$
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None of the above
Explanation
$$5x^{3} + 5x^{2} + 4x + 3 + 4x^{2} + 5x$$
$$=5x^{3} + 9x^{2} + 9x + 3$$
If we add $$7x$$ and $$5y^2+z$$ , what will be the result?
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binomial
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trinomial
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polynimial
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can"t be determind
Explanation
$$(7x)+(5y^2+z) =7x+5y^2+z$$ is a trinomial
If we add $$3+7x$$ and $$11x$$ , what will be the result?
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monomial
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binominal
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trinimial
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can"t be determined
Explanation
$$(3+7x)+11x=3+18x$$ is a binomial.
Find an equivalent simplified expression for $$\displaystyle 2\left( 4x+7 \right) -3\left( 2x-4 \right) $$.
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$$\displaystyle x+2$$
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$$\displaystyle 2x+2$$
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$$\displaystyle 2x+26$$
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$$\displaystyle 3x+10$$
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$$\displaystyle 3x+11$$
Explanation
The value of $$2(4x+7)-3(2x-4)$$
$$\Rightarrow 8x+14-6x+12$$
$$\Rightarrow 2x+26$$
The expression $$\left( { x }^{ 2 }y-3{ y }^{ 2 }+5x{ y }^{ 2 } \right) -\left( -{ x }^{ 2 }y+3x{ y }^{ 2 }-3{ y }^{ 2 } \right) $$ is equivalent to which of the following expression?
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$$4{ x }^{ 2 }{ y }^{ 2 }$$
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$$8x{ y }^{ 2 }-6{ y }^{ 2 }$$
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$$2{ x }^{ 2 }y+2x{ y }^{ 2 }$$
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$$2{ x }^{ 2 }y+8x{ y }^{ 2 }-6{ y }^{ 2 }$$
Explanation
We have,
$$(x^2y-3y^2+5xy^2)-(-x^2y+3xy^2-3y^2) $$
$$= x^2y-3y^2+5xy^2+x^2y-3xy^2+3y^2$$
$$=2x^2y+2xy^2$$
Therefore, option C is correct.
Simplify the expression: $$\displaystyle { t }^{ 2 }-59t+54-82{ t }^{ 2 }+60t$$
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$$\displaystyle -26{ t }^{ 2 }$$
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$$\displaystyle -26{ t }^{ 6 }$$
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$$\displaystyle -81{ t }^{ 4 }+{ t }^{ 2 }+54$$
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$$\displaystyle -81{ t }^{ 2 }+{ t }+54$$
Explanation
$$t^2-59t+45-82t^2+60t$$
$$\Rightarrow t^2-82t^2+60t-59t+54$$
$$\Rightarrow -81t^2+t+54$$
$$ \left( a+2b+3c \right) -\left( 4a+6b-5c \right) $$ is equivalent to:
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$$ -4a-8b-2c$$
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$$ -4a-4b+8c$$
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$$ -3a+8b-2c$$
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$$-3a-4b-2c$$
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$$ -3a-4b+8c$$
Explanation
The value of $$(a+2b+3c)-(4a+6b-5c)$$
$$\Rightarrow a+2b+3c-4a-6b+5c$$
$$\Rightarrow -3a-4b+8c$$
Simplify: $$\left( -3p{ q }^{ 2 }+4pq \right) -\left( 7pq-9p{ q }^{ 2 } \right) $$
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$$6p{ q }^{ 2 }+3pq$$
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$$6p{ q }^{ 2 }-3pq$$
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$$-12p{ q }^{ 2 }+3pq$$
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$$-12p{ q }^{ 2 }-3pq$$
Explanation
$$\left ( -3pq^{2}+4pq \right )-\left ( 7pq-9pq^{2} \right )$$
$$=-3pq^{2}+4pq-7pq+9pq^{2}$$
$$=-3pq^{2}+9pq^{2}+4pq-7pq$$
$$=6pq^{2}-3pq$$
Simplify :$$\left( -8pst+3prq-14 \right) -\left( 7prq-20+2pst \right) =$$
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$$6-10pst+10prq$$
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$$6-10pst-4prq$$
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$$-6pst-10prq+6$$
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$$-10pst-4prq-34$$
Explanation
$$(-8pst+3prq-14)-(7prq-20+2pst)$$
$$=-8pst+3prq-14-7prq+20-2pst$$
$$=-8pst-2pst+3prq-7prq-14+20$$
$$=-10pst-4prq+6$$
$$=6-10pst-4prq$$
What must be subtracted from $$3{ x }^{ 2 }+4{ y }^{ 2 }-5$$ to get $$2{ x }^{ 2 }-3{ y }^{ 2 }+5$$?
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$${ x }^{ 2 }+3{ y }^{ 2 }+5$$
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$${ x }^{ 2 }-4{ y }^{ 2 }+5$$
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$${ x }^{ 2 }+7{ y }^{ 2 }-10$$
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$${ x }^{ 2 }-7{ y }^{ 2 }-10$$
Explanation
Subtract both expression to get the answer
$$\Rightarrow \left ( 3x^{2}+4y^{2}-5 \right )-\left ( 2x^{2}-3y^{2}+5 \right )$$
$$=3x^{2}+4y^{2}-5-2x^{2}+3y^{2}-5$$
$$=3x^{2}-2x^{2}+4y^{2}+3y^{2}-5-5$$
$$=x^{2}+7y^{2}-10$$
The sum of $$3$$ expression is $$8+13a+7a^$$ Two of them are $$ 2a^2+3a+2$$ and $$ 3a^2-4a+1$$ . Find the third expression.
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$$a^2+a+5$$
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$$2a^2+a+5$$
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$$2a^3+14a+5$$
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$$2a^2+14a+5$$
Explanation
Expression be x
$$\Rightarrow x+(2a^2+3a+2)+(3a^2-4a+1)$$
$$=8+13a+7a^2$$
$$=x+5a^2-a+3$$
$$=8+13a+7a^2$$
$$\Rightarrow x=7a^2+13a+8-5a^2+a-3$$
$$x=2a^2+14a+5$$.
Simplify :
$$({a}^{3} - 2{a}^{2} + 4a - 5) - (- {a}^{3} - 8a + 2{a}^{2} + 5)$$
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$$2{a}^{3} + 7{a}^{2} + 6a - 10$$
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$$2{a}^{3} + 7{a}^{2} + 12a - 10$$
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$$2{a}^{3} - 4{a}^{2} + 12a - 10$$
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$$2{a}^{3} - 4{a}^{2} + 6a - 10$$
Explanation
$$({a}^{3} - 2{a}^{2} + 4a - 5) - (- {a}^{3} - 8a + 2{a}^{2} + 5)$$
= $${a}^{3} - 2{a}^{2} + 4a - 5 + {a}^{3} + 8a - 2{a}^{2} - 5$$
= $$2{a}^{3} - 4{a}^{2} + 12a - 10$$
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