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CBSE Questions for Class 7 Maths Algebraic Expressions Quiz 4 - MCQExams.com
CBSE
Class 7 Maths
Algebraic Expressions
Quiz 4
An expression is taken away from $$3x^{2} - 4y^{2} + 5xy + 20$$ to obtain $$-x^{2} - y^{2} + 6xy + 20$$, then the expression is __________.
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$$4x^{2} - 3y^{2} - xy$$
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$$2x^{2} - 5y^{2} + xy + 40$$
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$$3y^{2} - xy - 4x^{2}$$
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$$4x^{2} + 3y^{2} + xy$$
Explanation
We are given two expression
$$3x^{2}-4y^{2}+5xy+20$$ ................................(1)
$$-x^{2}-y^{2}+6xy+20$$ ................................(2)
An expression is taken away from (1) to obtain (2) is given by
$$3x^{2}-4y^{2}+5xy+20 - (-x^{2}-y^{2}+6xy+20)$$
$$ = 3x^{2}-4y^{2}+5xy+20 +x^{2}+y^{2}-6xy-20)$$
$$ = 4x^{2}-3y^{2}-xy$$
Simplify : $$(a^{3} - 2a^{2} + 4a - 5) - (-a^{3} - 8a + 2a^{2} + 5)$$.
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$$2a^{3} + 7a^{2} + 6a - 10$$
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$$2a^{3} + 7a^{2} + 12a - 10$$
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$$2a^{3} - 4a^{2} + 12a - 10$$
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$$2a^{3} - 4a^{2} + 6a - 10$$
Explanation
We need to simplify $$(a^{3}-2a^{2}+4a-5) - (-a^{3}-8a+2a^{2}+5)$$
$$=a^{3}-2a^{2}+4a-5 +a^{3}+8a-2a^{2}-5$$
$$=(a^{3}+a^{3})+(-2a^{2}-2a^{2})+(4a+8a)-10$$
$$=2a^{3}-4a^{2}+12a-10$$
By how much is $${a}^{4} + 4{a}^{2}{b}^{2} + {b}^{4}$$ more than $${a}^{4} - 8{a}^{2}{b}^{2} + {b}^{4}$$?
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$$12{a}^{2}{b}^{2}$$
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$$-12{a}^{2}{b}^{2}$$
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$$2{a}^{4} + 2{b}^{4}$$
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$$10{a}^{2}{b}^{2}$$
Explanation
Required expression
$$= ({a}^{4} + 4{a}^{2}{b}^{2} + {b}^{4}) - ({a}^{4} - 8{a}^{2}{b}^{2} + {b}^{4}$$)
$$={a}^{4} + 4{a}^{2}{b}^{2} + {b}^{4} - {a}^{4} + 8{a}^{2}{b}^{2} - {b}^{4}$$
$$=12{a}^{2}{b}^{2}$$
Subtract $$(2a - 3b + 4c)$$ from the sum of $$(a + 3b - 4c), (4a - b + 9c)$$ and $$(-2b + 3c - a)$$.
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$$3a + 2b + 4c$$
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$$2a - 2b + 4c$$
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$$3a - 4b - 2c$$
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$$2a + 3b + 4c$$
Explanation
It is instructed to subtract $$(2a - 3b + 4c)$$ from the sum of $$(a + 3b - 4c), (4a - b + 9c)$$ and $$(-2b + 3c - a)$$.
So, First we will do the sum of the three given polynomials,
Sum $$= (a + 3b - 4c) + (4a - b + 9c) + (-2b + 3c - a)$$
$$= (a + 4a - a)+ (3b - b - 2b) + (-4c + 9c + 3c)$$
$$= 4a + 8c$$
Now, we can perform the subtraction,
$$\therefore$$ Required difference
$$= (4a + 8c) - (2a - 3b + 4c)$$
$$= 4a + 8c - 2a + 3b - 4c$$
$$= 2a + 3b + 4c$$
Add the following:
$$2{p}^{2}{q}^{2}-3pq+4, 5+7pq-3{p}^{2}{q}^{2}$$
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$$-p^2q^2-4pq+9$$
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$$-p^2q^2+4pq+9$$
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$$-p^2q^2+2pq-9$$
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None of these
Explanation
$$2{p}^{2}{q}^{2}-3pq+4+5+7pq-3{p}^{2}{q}^{2}$$
$$=2p^2q^2-3p^2q^2-3pq+7pq+9$$
$$=-p^2q^2+4pq+9$$
add $$2x$$ and $$3x$$:-
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$$9x$$
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$$3x$$
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$$5x$$
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$$7x$$
Explanation
$$2x+3x=(2+3)x=5x$$
State true or false
We can add or subtract like terms in an algebraic expression.
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True
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False
Explanation
We can always subtract like terms in an algebraic expression and same is true for addition.
Ex: Let $$ax^2-bx^2+cx+dx+e= 0$$ is a algebraic expression then this can be writtens as $$x^2(a-b)+x(c+d)+e=0$$
Answer : $$(A)$$
If we subtract a monomial from a binomial, then answer is atleast a binomial
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True
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False
Explanation
Consider a binomial $$-2xy+z$$ and a monomial $$-z$$.
If we add $$-2xy+z$$ and $$-z$$, we get
$$-2xy+z+-z=-2xy$$, which is a monomial.
So the result need not be a binomial.
$$\textbf{Hence, the given statement is False.}$$
Sum of $${x}^{2}+x$$ and $$y+{y}^{2}$$ is $$2{x}^{2}+2{y}^{2}$$
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True
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False
Explanation
The sum of $$x^{2}+x$$ and $$y+y^{2}$$ is given by
$$\left(x^{2}+x\right)+\left(y+y^{2}\right)=x^{2}+y^{2}+x+y$$
Therefore, Sum of $$x^{2}+x$$ and $$y+y^{2}$$ is not $$2 x^{2}+2 y^{2}$$.
$$\textbf{Hence, the given statement is False.}$$
State True or False:When we add a monomial and a trinomial, then answer can be a monomial.
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True
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False
Explanation
Consider a trinomial $$3xy+x+5$$ and monomial $$-x$$ and $$3xy$$
$$\bullet$$ If we subtract $$3xy$$ from $$3xy+x+5$$, we get $$x+5$$ which is a binomial
$$\bullet$$ if we subtract $$-x$$ from $$3xy+x+5$$, we get $$3xy+2x+5$$ which is a trinomial..
We know that, a binomial or a trinomial is a polynomial.
Therefore, when we subtract a monomial from a trinomial, then answer will be a polynomial.
$$\textbf{Hence, given statement is True.}$$
The sum of $$-7pq$$ and $$2pq$$ is
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$$-9pq$$
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$$ \ 9pq $$
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$$\ 5pq $$
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$$ - 5pq$$
Explanation
Guven monomials are $$-7pq$$ and $$2pq$$
$$\therefore$$ Required sum $$=(- 7pq) + (2pq )$$
$$-7pq+2q$$
$$= (-7+2) pq\qquad[\because -7pq$$ and $$2pq$$ are like terms $$]$$
$$ = -5pq$$
Hence, the correct answer is option (D).
If we subtract $$-3x^{2}y^{2}$$ from $$x^{2}y^{2}$$, then we get
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$$ - 2x^{2}y^{2}$$
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$$-4x^{2}y^{2} $$
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$$ 2x^{2}y^{2}$$
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$$ 4x^{2}y^{2}$$
Explanation
Given monomials are : $$-3x^{2}y^{2}$$ from $$x^{2}y^{2}$$
Required difference $$=(x^2y^2)-(-3x^2y^2)$$
$$=x^2y^2+3x^2y^2$$
$$=(1+3)x^2y^2$$ [Since the given monomials are like terms]
$$=4x^{2}y^{2}$$
Hence, option (D) is the correct answer.
Sum of $$a-b + ab$$ , $$b +c-bc$$ and $$c -a-ac$$ is
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$$2c+ab-ac-bc$$
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$$ 2c - ab-ac-bc$$
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$$2c+ab+ac+bc$$
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$$ 2c -ab+ac + bc$$
Explanation
Sum of $$a-b + ab$$ , $$b +c-bc$$ and $$c -a-ac$$
$$=(a-b+ab)+(b-c-bc)+(c-a-ac)$$
$$=a-b+ab+b+c-bc+c-a-ac$$
Rearranging and collecting like terms,
$$=a-a-b+b+c+c+ab-bc-ac$$
$$=2c+ab-ac-bc$$
Hence, option (A) is correct.
$$-xy-(-5xy)$$ is equal to
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$$-6xy$$
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$$6xy$$
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$$-4xy$$
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$$4xy$$
Explanation
$$\begin{aligned}{} - xy - ( - 5xy) &= - xy + 5xy\\& = ( - 1 + 5)xy\\ &= 4xy\end{aligned}$$
State the following statement is true or false.
Sum of $$2$$ and $$p$$ is $$2p$$.
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True
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False
Explanation
Sum of $$2$$ and $$p$$ is $$2+p$$ not $$2p$$.
Simplify: $$\displaystyle { 2x }^{ 2 }y-{ 3xy }^{ 2 }+{ 2x }^{ 2 }y-{ 4x }^{ 2 }y+{ 2xy }^{ 2 }$$
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$$\displaystyle { 4x }^{ 2 }y+{ 2xy }^{ 2 }$$
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$$\displaystyle { 2x }^{ 2 }y-8xy$$
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$$-xy^2$$
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$$-xy-2x+y^2$$
Explanation
$$\displaystyle { 2x }^{ 2 }y-{ 3xy }^{ 2 }+{ 2x }^{ 2 }y-{ 4x }^{ 2 }y+{ 2xy }^{ 2 }$$
$$\displaystyle =\left( { 2x }^{ 2 }y+{ 2x }^{ 2 }y-{ 4x }^{ 2 }y \right) +\left( -{ 3xy }^{ 2 }+{ 2xy }^{ 2 } \right) , $$ (Arranging like terms together)
$$\displaystyle =0-{ xy }^{ 2 }=-{ xy }^{ 2 }$$
Hence simplified form of the given expression is $$-xy^2$$
From the sum of $$z^3+3z^2+5z+8$$ and $$4z^3+2z^2-7z-2$$ subtract $$2z^3-3z^2+z-4$$.
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$$0$$
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$$8z^2-3z$$
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$$3z^3+8z^2-3z+10$$
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$$2-z$$
Explanation
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,
$$5z^3+5z^2-2z+6$$
$$-(2z^3-3z^2+z-4)$$
$$=5z^3+5z^2-2z+6$$
$$-2z^3+3z^2-z+4$$
$$=3z^3+8z^2-3z+10$$
$$If \:x^2 + 2x = 45, what \: is \: the\: value \: of \: x^4 + 4x^3 + 4x^2 - 13?$$
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2013
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1986
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2012
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32
Subtract the second expression from the first:
$$5x^2-6xy+2$$ and $$3x^2+10xy-8$$.
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$$x^2-16xy-10$$
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$$2x^2+86xy+10$$
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$$x^2-8xy- 50$$
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$$2x^2-16xy+10$$
Explanation
$$(5x^2-6xy+2) - (3x^2+10xy-8)$$
$$=5x^2-6xy+2-3x^2-10xy+8$$
$$=2x^2-16xy+10$$
Subtract $$4a -7ab + 3b + 12$$ from $$12a- 9ab + 5b- 3$$.
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$$8a+2ab + 2b+15$$
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$$8a + 2b+15$$
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$$8a-2ab + 2b+15$$
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$$8a-2ab + 2b-15$$
Explanation
subtract $$4a - 7ab + 3b + 12$$ from $$12a- 9ab + 5b - 3$$
$$=12a- 9ab + 5b - 3-(4a - 7ab + 3b+12)$$
$$=12a- 9ab + 5b - 3-4a +7ab - 3b-12$$
$$=8a-2ab+2b-15$$
From $$\displaystyle 8-y+{ 2y }^{ 2 }$$ take away $$\displaystyle \left( { y }^{ 2 }-7-2y \right) $$.
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$$y^2+y+15$$
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$$5y^2-1$$
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$$3y-7y^2+11$$
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None of these
Explanation
Here we have to just subtract $$y^2-7-2y$$ from $$8-y+2y^2$$
$$\therefore \displaystyle \left( 8-y+{ 2y }^{ 2 } \right) -\left( { y }^{ 2 }-7-2y \right) =8-y+{ 2y }^{ 2 }-{ y }^{ 2 }+7+2y$$
$$=\displaystyle \left( 8+7 \right) +\left( -y+2y \right) +\left( { 2y }^{ 2 }-{ y }^{ 2 } \right) $$
$$\displaystyle =15+y+{ y }^{ 2 }$$
Hence, required value is $$y^2+y+15$$.
What should be subtracted from $$2a+6b-5$$ to get $$-3a+2b+3$$?
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$$5+4b-8$$
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$$5a+4b-8$$
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$$5a+4ab-8$$
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$$5a+4b-10$$
Explanation
Let $$X=-3a+2b+3$$ and $$Y=2a+6b-5$$
Let $$Z$$ be the required expression
Now, $$X=Y-Z$$
$$=>Z=Y-X$$
Thus,
$$2a+6b-5-(-3a+2b+3)$$
$$=2a+6b-5+3a-2b-3$$
$$=5a+4b-8$$
Find the sum of $$\displaystyle { x }^{ 2 }-{ 2y }^{ 2 },{ 2x }^{ 2 }-4xy+{ 5y }^{ 2 },{ 6y }^{ 2 }+11xy-{ 6x }^{ 2 }$$
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$$x^2-5xy+2y^2$$
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$$5y^2+2xy-2x^2$$
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$$9y^2+7xy-3x^2$$
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$$2x^2-7xy+y^2$$
Explanation
Required sum $$=\displaystyle { (x }^{ 2 }-{ 2y }^{ 2 })+{ (2x }^{ 2 }-4xy+{ 5y }^{ 2 })+{ (6y }^{ 2 }+11xy-{ 6x }^{ 2 })$$
$$=\displaystyle \left( { x }^{ 2 }+{ 2x }^{ 2 }-{ 6x }^{ 2 } \right) +\left( { -2y }^{ 2 }+{ 5y }^{ 2 }+{ 6y }^{ 2 } \right) +\left( -4xy+11xy \right) $$ (Combining like terms)
$$\displaystyle= -{ 3 }x^{ 2 }+{ 9y }^{ 2 }+7xy$$.
What should be added to $$5x^2+2xy+y^2$$ to get $$3x^2+4xy$$?
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$$-2x^2+2xy-y^2$$
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$$x^2+2y-y^2$$
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$$-2x^2+2y-xy^2$$
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$$x^2+2xy-y^2$$
Explanation
Let $$A=3x^2+4xy$$ and $$B=5x^2+2xy+y^2$$
Let $$C$$ be the required expression
Now, $$A=B+C$$
$$=>C=A-B$$
Thus, $$3x^2+4xy-(5x^2+2xy+y^2)$$
$$=3x^2+4xy-5x^2-2xy-y^2$$
$$=-2x^2+2xy-y^2$$
Subtract $$(5x^{2}-5x-7)$$ from the sum of $$(x^{2}-3),\:(5-4x)$$ and $$(9+4x^{2})$$
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$$x+18$$
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$$x^{2}+x+10$$
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$$-x+24$$
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$$-9x+18$$
Explanation
$$(x^2-3)+(5-4x)+(9+4x^2)=5x^2-4x+11$$
Now, $$(5x^2-4x+11)-(5x^2-5x-7)=x+18$$
Option A is correct.
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
$$\displaystyle 3^{3}-2a^{2}+4a-5$$
$$\displaystyle (-)-a^{3}+2a^{2}-8a+5$$
+ - + -
$$\displaystyle \underline{\overline{2a^{3}-4a^{2}+12a-10}}$$
Simplify : $$\displaystyle 5x-\left[ 4x-\left\{ \left( 2x-5 \right) -3\left( 3x-4 \right) \right\} \right] $$
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$$\displaystyle -7-6x$$
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$$\displaystyle -7+6x$$
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$$\displaystyle 7+6x$$
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$$\displaystyle 7-6x$$
Explanation
$$\displaystyle 5x-\left[ 4x-\left\{ \left( 2x-5 \right) -3\left( 3x-4 \right) \right\} \right] $$
$$=5x-4x+[(2x-5)-3(3x-4)]$$
$$=5x-4x+2x-5-9x+12$$
$$=7-6x$$
$$\displaystyle -a-[a+\{ { a+b-2a-(a-2b)\} }-b]$$ is equal to
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$$\displaystyle -4a+b$$
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$$\displaystyle 4a-2b$$
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$$0$$
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$$\displaystyle -2b$$
Explanation
Given, $$\displaystyle -a-[a+\{ { a+b-2a-(a-2b)\} }-b]$$
=$$\displaystyle -a-[a+\{ { a+b-2a-a+2b\} }-b]$$
$$\displaystyle =-a-[a+\{ { -2a+3b\} }-b]$$
$$\displaystyle =-a-\left[ a-2a+3b-b \right] $$
$$\displaystyle =-a-\left[ -a+2b \right] $$
$$\displaystyle =-a+a-2b$$
$$\displaystyle =-2b$$, which is simplified form of the given expression.
By how much is $$\displaystyle x^{4}-4x^{2}y^{2}+y^{4}$$ less than $$\displaystyle x^{4}+8x^{2}y^{2}+y^{4}$$?
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$$\displaystyle -12x^{2}y^{2}$$
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$$\displaystyle 12x^{2}y^{2}$$
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$$\displaystyle -12xy$$
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$$\displaystyle 12xy$$
Explanation
We have to find solution of
$$( x^{4}+8x^{2}y^{2}+y^{4})$$ $$-(x^{4}-4x^{2}y^{2}+y^{4})$$
Separating like terms and unlike terms, we get
$$=$$ $$x^4 - x^4 +y^4 - y^4 +8x^2y^2-(-4x^2y^2)$$
$$=$$ $$8x^2y^2 + 4x^2y^2$$
$$=$$ $$12x^2y^2$$
Subtract the sum of $$\displaystyle \left( { 5x }^{ 2 }-7x+4 \right) $$ and $$\displaystyle \left( 2x-{ 5x }^{ 3 }+1 \right) $$ from $$\displaystyle \left( { 3x }^{ 2 }-1+5x \right) $$.
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$$\displaystyle { 5x }^{ 3 }+{ 11x }^{ 2 }-5x+3$$
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$$5x^3-2x^2+10x-6$$
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$$\displaystyle { 3x }^{ 3 }+{ 11x }^{ 2 }+3x+5$$
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$$\displaystyle { 11x }^{ 3 }+{ 3x }^{ 2 }+5x-3$$
Explanation
$$3x^2 - 1 + 5x - [(5x^2-7x+4) + (2x-5x^3+1)]$$
= $$3x^2 - 1 +5x - [5x^2-5x+5- 5x^3]$$
= $$3x^2 - 1 +5x - 5x^2+5x-5 +5x^3$$
=$$ -2x^2 + 10x -6 + 5x^3$$
= $$5x^3 -2x^2 + 10x - 6$$
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