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CBSE Questions for Class 8 Maths Factorisation Quiz 4 - MCQExams.com
CBSE
Class 8 Maths
Factorisation
Quiz 4
Factorise:
$$x^3 -3x^2+x-3$$
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0%
$$(x^2 + 7)(x-3)$$
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$$(x^2 + 1)(x-3)$$
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$$(x^2 - 1)(x-2)$$
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$$(x^2 + 7)(x-2)$$
Explanation
$$x^3 -3x^2+x-3$$
$$=x^2(x-3)+1(x-3)$$
$$=(x^2 + 1)(x-3)$$
Factorise:
$$ab^2 + (a-1)b -1$$
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$$(b+ 1) (a-1)$$
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$$(b+ 1) (b-1)$$
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$$(b+ 1) (ab-1)$$
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$$(b- 1) (ab-1)$$
Explanation
$$ab^2 + (a-1)b -1$$
$$=ab^2+ab-b-1$$
$$=ab(b+1)-1(b+1)$$
$$=(b+ 1) (ab-1)$$
Factorise: $$9x^3-6x^2+ 12x$$
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$$3x (3x^2-2x + 4)$$
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$$x (3x^2-2x + 4)$$
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$$x (3x^2-2x - 4)$$
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$$3x (3x^2-x + 7)$$
Explanation
factorising $$9x^3-6x^2+ 12x$$
Take $$3x$$ as common,
$$=3x (3x^2-2x + 4)$$
Factorise:
$$12x + 15$$
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$$3(4x + 5)$$
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$$(4x + 5)$$
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$$3(4x - 5)$$
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None of the Above
Explanation
$$12x + 15$$
Taking 3 as common,
$$3(4x + 5)$$
Answer $$3(4x + 5)$$
Factorise:
$$6a(a -2b) + 5b(a -2b)$$
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0%
$$(a-b) (6a + 5b)$$
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$$(a-2b) (6a + 5b)$$
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$$(a-2b) (3a + 5b)$$
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$$(a-b) (3a + 5b)$$
Explanation
$$6a(a -2b) + 5b(a -2b)$$
taking (a -2b) common,
$$=(a-2b) (6a + 5b)$$
Evaluate: $$\displaystyle \left( { 7a }^{ 2 }-5a \right) \div 5a$$
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0%
$$\displaystyle 7a-1$$
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$$\displaystyle 7a-5$$
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$$\displaystyle \frac { 1 }{ 5 } \left( 7a-5 \right) $$
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$$\displaystyle \frac { 1 }{ 5 } \left( 7a-1 \right) $$
Explanation
$$\displaystyle \left( { 7a }^{ 2 }-5a \right) \div 5a=\frac { { 7a }^{ 2 }-5a }{ 5a }$$
=$$\dfrac { a\left( 7a-5 \right) }{ 5a } =\dfrac { 1 }{ 5 } \left( 7a-5 \right) $$
Evaluate: $$\displaystyle ( 6{ x }^{ 2 }-4x) \div 2x$$
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$$\displaystyle 2x-3$$
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$$\displaystyle 3x-2$$
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$$\displaystyle 3{ x }^{ 2 }-2$$
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$$\displaystyle 12x-8$$
Explanation
$$\displaystyle \left( 6{ x }^{ 2 }-4x \right) \div 2x=\frac { 6{ x }^{ 2 }-4x }{ 2x } $$
$$=\dfrac { 2x\left( 3x-2 \right) }{ 2x } $$
$$\displaystyle =3x-2$$
Simplify: $$\displaystyle \left( 12a-36 \right) \div 6$$
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$$\displaystyle 2a+6$$
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$$\displaystyle a-3$$
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$$\displaystyle 2a-6$$
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$$\displaystyle a+3$$
Explanation
$$\displaystyle \left( 12a-36 \right) \div 6=\frac { 12a-36 }{ 6 } =\frac { 12\left( a-3 \right) }{ 6 } $$
$$\displaystyle =2\left( a-3 \right) $$
$$\displaystyle =2a-6$$
Simplify: $$\displaystyle 9\left( { a }^{ 4 }{ b }^{ 6 }-{ a }^{ 6 }{ b }^{ 4 } \right) \div 3{ a }^{ 4 }{ b }^{ 4 }$$
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$$\displaystyle 3(b-a)$$
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$$\displaystyle 3(a-b)$$
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$$\displaystyle 3\left( { a }^{ 2 }-{ b }^{ 2 } \right) $$
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$$\displaystyle 3\left( { b }^{ 2 }-{ a }^{ 2 } \right) $$
Explanation
$$\displaystyle 9\left( { a }^{ 4 }{ b }^{ 6 }-{ a }^{ 6 }{ b }^{ 4 } \right) \div 3{ a }^{ 4 }{ b }^{ 4 }=\frac { 9\left( { a }^{ 4 }{ b }^{ 6 }-{ a }^{ 6 }{ b }^{ 4 } \right) }{ 3{ a }^{ 4 }{ b }^{ 4 } } $$
$$\displaystyle =\frac { 9{ a }^{ 4 }{ b }^{ 4 }\left( { b }^{ 2 }-{ a }^{ 2 } \right) }{ 3{ a }^{ 4 }{ b }^{ 4 } } $$
$$\displaystyle = 3\left( { b }^{ 2 }-{ a }^{ 2 } \right) $$
Divide: $$\displaystyle \left( { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 }-{ z }^{ 6 }{ y }^{ 7 }{ x }^{ 8 } \right) $$ by $$\displaystyle { y }^{ 7 }{ x }^{ 8 }{ z }^{ 6 }$$
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$$\displaystyle -1$$
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$$\displaystyle 1$$
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$$\displaystyle 0$$
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$$\dfrac 12$$
Explanation
$$\displaystyle \left( { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 }-{ z }^{ 6 }{ y }^{ 7 }{ x }^{ 8 } \right) \div { y }^{ 7 }{ x }^{ 8 }{ z }^{ 6 }$$
$$\displaystyle =\frac { { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 }-{ x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 } }{ { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 } } =\frac { 0 }{ { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 } } =0$$
Evaluate: $$\displaystyle \left( 4{ x }^{ 8 }-{ 5x }^{ 6 }+{ 6x }^{ 4 } \right) \div { x }^{ 4 }$$
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$$\displaystyle { 4x }^{ 4 }-{ 5x }^{ 10 }+6x$$
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$$\displaystyle { 4x }^{ 5 }-{ 5x }^{ 3 }+6x$$
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$$\displaystyle { 4x }^{ 3 }-5x+6$$
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$$\displaystyle { 4x }^{ 4 }-{ 5x }^{ 2 }+6$$
Explanation
$$\displaystyle \left( 4{ x }^{ 8 }-{ 5x }^{ 6 }+{ 6x }^{ 4 } \right) \div { x }^{ 4 }=\frac { 4{ x }^{ 8 }-{ 5x }^{ 6 }+{ 6x }^{ 4 } }{ { x }^{ 4 } } $$
$$\displaystyle =\frac { { x }^{ 4 }\left( { 4x }^{ 4 }-{ 5x }^{ 2 }+6 \right) }{ { x }^{ 4 } } $$
$$\displaystyle ={ 4x }^{ 4 }-{ 5x }^{ 2 }+6$$
Simplify: $$\displaystyle \left( { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }-{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }+{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } \right) \div { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }$$
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$$\displaystyle 1$$
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$$\displaystyle -1$$
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$$\displaystyle 0$$
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None of these
Explanation
$$\displaystyle \left( { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }-{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }+{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } \right) \div { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }$$
$$\displaystyle =\frac { { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }-{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }+{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } }{ { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } } $$
$$= \dfrac {0 + a^2b^2c^3}{a^2b^2c^3}$$
$$\displaystyle =\frac { { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } }{ { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } } =1$$
Divide: $$\displaystyle \left( -16{ x }^{ 6 }-24{ x }^{ 4 } \right) $$ by $$\displaystyle \left( -{ 8x }^{ 3 } \right) $$
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0%
$$\displaystyle { 2x }^{ 3 }+3x$$
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$$\displaystyle { 2x }^{ 2 }+3$$
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$$\displaystyle -{ 2x }^{ 3 }-3x$$
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$$\displaystyle -{ 2x }^{ 2 }-3$$
Explanation
$$\displaystyle \left( -16{ x }^{ 6 }-24{ x }^{ 4 } \right) \div \left( -{ 8x }^{ 3 } \right) =\frac { -16{ x }^{ 6 }-24{ x }^{ 4 } }{ -{ 8x }^{ 3 } } $$
$$\displaystyle =\frac { -8{ x }^{ 4 }\left( { 2x }^{ 2 }+3 \right) }{ { 8x }^{ 3 } } $$
$$\displaystyle =x\left( { 2x }^{ 2 }+3 \right) $$
$$\displaystyle = { 2x }^{ 3 }+3x$$
Evaluate : $$\displaystyle 21{ x }^{ 3 }{ y }^{ 3 }+35{ x }^{ 4 }{ y }^{ 2 }-56{ x }^{ 2 }{ y }^{ 4 }\div -7{ x }^{ 2 }{ y }^{ 2 }$$
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$$\displaystyle -5{ x }^{ 2 }+3xy+8{ y }^{ 2 }$$
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$$\displaystyle 8{ y }^{ 2 }-3xy-5{ x }^{ 2 }$$
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$$\displaystyle 5{ x }^{ 2 }+3xy-8{ y }^{ 2 }$$
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$$\displaystyle 5{ x }^{ 2 }-3xy+8{ y }^{ 2 }$$
Explanation
$$\displaystyle 21{ x }^{ 3 }{ y }^{ 3 }+35{ x }^{ 4 }{ y }^{ 2 }-56{ x }^{ 2 }{ y }^{ 4 }\div -7{ x }^{ 2 }{ y }^{ 2 }$$
$$\displaystyle = \frac { 21{ x }^{ 3 }{ y }^{ 3 }+35{ x }^{ 4 }{ y }^{ 2 }-56{ x }^{ 2 }{ y }^{ 4 } }{ -7{ x }^{ 2 }{ y }^{ 2 } } $$
$$\displaystyle = \frac { 7{ x }^{ 2 }{ y }^{ 2 }\left( 3xy+5{ x }^{ 2 }-8{ y }^{ 2 } \right) }{ -7{ x }^{ 2 }{ y }^{ 2 } } $$
$$\displaystyle =-\left( 3xy+5{ x }^{ 2 }-8{ y }^{ 2 } \right) $$
$$\displaystyle = 8{ y }^{ 2 }-3xy-5{ x }^{ 2 }$$
Factorisation of the expression $$\displaystyle -15x+5{ x }^{ 3 }$$ gives result as
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0%
$$\displaystyle 5x( 3-{ x }^{ 2 }) $$
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$$\displaystyle 5x( { x }^{ 2 }-3) $$
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$$\displaystyle -5x( { x }^{ 2 }-3 ) $$
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$$\displaystyle x( { x }^{ 2 }-3) $$
Explanation
$$\displaystyle -15x+5{ x }^{ 3 }=\left( -5\times 3\times x \right) +\left( 5\times x\times x\times x \right) $$
$$\displaystyle = -5x( 3-{ x }^{ 2 }) $$
$$\displaystyle = 5x ( { x }^{ 2 }-3) $$
Divide: $$\displaystyle 8\left( { x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 } \right) \div 2{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }$$
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$$\displaystyle 4(y+z)$$
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$$\displaystyle 4(x)$$
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$$\displaystyle 4(x+y+z)$$
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$$\displaystyle 4x+4y+z$$
Explanation
$$\displaystyle 8\left( { x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 } \right) \div 2{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }$$
$$\displaystyle =\frac { 8\left( { x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 } \right) }{ 2{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 } } $$
$$\displaystyle =\frac { 8{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }\left( x+y+z \right) }{ 2{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 } } $$
$$\displaystyle =4\left( x+y+z \right) $$
Find the value of $$\displaystyle \left( { 3x }^{ 3 }+{ 2x }^{ 2 }+x \right) \div 4x$$
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$$\displaystyle { 3x }^{ 2 }+2x+1$$
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$$\displaystyle \frac { 1 }{ 4 } \left( { 3x }^{ 2 }+2x+1 \right) $$
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$$\displaystyle { 3x }^{ 2 }+2x+\frac { 1 }{ 4 } $$
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$$\displaystyle 3x+2$$
Explanation
$$\displaystyle \left( { 3x }^{ 3 }+{ 2x }^{ 2 }+x \right) \div 4x=\frac { { 3x }^{ 3 }+{ 2x }^{ 2 }+x }{ 4x } $$
$$\displaystyle =\frac { x\left( { 3x }^{ 2 }+2x+1 \right) }{ 4x } $$
$$\displaystyle =\frac { 1 }{ 4 } \left( { 3x }^{ 2 }+2x+1 \right) $$
Find the value of $$\displaystyle \left( { 7a }^{ 6 }-8{ a }^{ 5 }+9{ a }^{ 4 } \right) \div { a }^{ 3 }$$
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0%
$$\displaystyle { 7a }^{ 3 }-{ 8a }^{ 2 }+9a$$
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$$\displaystyle { 7a }^{ 2 }-8a+9$$
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$$\displaystyle { 7a }^{ 4 }-{ 8a }^{ 2 }+9a$$
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$$\displaystyle { 7a }^{ 2 }-{ 8a }^{ 2 }+9a$$
Explanation
$$\displaystyle \left( { 7a }^{ 6 }-8{ a }^{ 5 }+9{ a }^{ 4 } \right) \div { a }^{ 3 }=\frac { { 7a }^{ 6 }-8{ a }^{ 5 }+9{ a }^{ 4 } }{ { a }^{ 3 } } $$
$$\displaystyle =\frac { { a }^{ 3 }\left( { 7a }^{ 3 }-{ 8a }^{ 2 }+9a \right) }{ { a }^{ 3 } } $$
$$\displaystyle = { 7a }^{ 3 }-{ 8a }^{ 2 }+9a$$
Solve: $$\displaystyle 3{ x }^{ 3 }-15{ x }^{ 2 }+21x\div 3x$$
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$$\displaystyle x+5+7x$$
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$$\displaystyle { x }^{ 2 }+5x+7$$
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$$\displaystyle 3{ x }^{ 2 }-5x+7$$
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$$\displaystyle { x }^{ 2 }-5x+7$$
Explanation
$$\displaystyle 3{ x }^{ 3 }-15{ x }^{ 2 }+21x\div 3x$$
$$\displaystyle = \frac { 3{ x }^{ 3 } }{ 3x } -\frac { 15{ x }^{ 2 } }{ 3x } +\frac { 21x }{ 3x } $$
$$\displaystyle ={ x }^{ 2 }-5x+7$$
Factorise : $$\displaystyle 40{ m }^{ 2 }n+50mn$$
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$$\displaystyle 10mn(4mn+5n)$$
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$$\displaystyle 10mn(2m+5)$$
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$$\displaystyle 10mn(2m+10)$$
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$$\displaystyle 10mn(4m+5)$$
Explanation
$$\displaystyle 40{ m }^{ 2 }n+50mn=\left( 2\times 5\times 2\times 2\times m\times m\times n \right) +\left( 2\times 5\times 5\times m\times n \right) $$
$$\displaystyle =10mn\left( 4m+5 \right) $$
Simplify: $$\displaystyle \left( 16{ x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+16{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 }+16{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 } \right) \div 8xyz$$
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$$\displaystyle 2\left( { x }^{ 2 }yz+xy{ z }^{ 2 }+x{ y }^{ 2 }z-xyz \right) $$
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$$\displaystyle \left( { x }^{ 2 }yz+xy{ z }^{ 2 }+x{ y }^{ 2 }z \right) $$
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$$\displaystyle 2{ x }^{ 2 }yz+2xy{ z }^{ 2 }+2x{ y }^{ 2 }z$$
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$$\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }z+2x{ y }^{ 2 }{ z }^{ 2 }+2{ x }^{ 2 }y{ z }^{ 2 }-xyz$$
Explanation
Given, $$\displaystyle \left( 16{ x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+16{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 }+16{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 } \right) \div 8xyz$$
$$\displaystyle =\frac { 16{ x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+16{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 }+16{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 } }{ 8xyz } $$
$$\displaystyle =\frac { 8xyz\left( 2{ x }^{ 2 }yz+2xy{ z }^{ 2 }+2x{ y }^{ 2 }z \right) }{ 8xyz } $$
$$\displaystyle =2{ x }^{ 2 }yz+2xy{ z }^{ 2 }+2x{ y }^{ 2 }z$$
Factorisation of the expression $$\displaystyle 6p-24q$$ results in :
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$$\displaystyle 6(p-4q)$$
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$$\displaystyle 6(p-q)$$
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$$\displaystyle 6(1-4q)$$
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$$\displaystyle 3(2-12q)$$
Explanation
$$\displaystyle 6p-24q=\left( 6\times p \right) -\left( 24\times q \right) $$
$$=\left( 6\times p \right) -\left( 6\times 4\times q \right) $$
$$=6\left( p-4q \right) $$
Which of the following statement is correct?
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$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-2 y \right) $$
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$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-2 \right) $$
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$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( 2x-2y \right) $$
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$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-y \right) $$
Explanation
$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x$$
$$=\dfrac { { x }^{ 2 }-2xy }{ x } =\dfrac { x\left( x-2y \right) }{ x } $$
$$=\left( x-2y \right) $$
$$\displaystyle \therefore \left( { x }^{ 2 }-2xy \right) \div x=\left( x-2y \right) $$ is a correct statement.
The value of $$(\displaystyle 9{ x }^{ 2 }+18x+27) \div 9$$ is equal to
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0%
$$\displaystyle x+2$$
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$$\displaystyle { x }^{ 2 }+2x+2$$
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$$\displaystyle { x }^{ 2 }+2x+3$$
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$$\displaystyle { x }^{ 2 }+2x+1$$
Explanation
$$(\displaystyle 9{ x }^{ 2 }+18x+27) \div 9 =\frac { 9{ x }^{ 2 }+18x+27 }{ 9 } $$
$$\displaystyle =\frac { 9\left( { x }^{ 2 }+2x+3 \right) }{ 9 } $$
$$\displaystyle = { x }^{ 2 }+2x+3$$
Which of the following is incorrect?
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$$\displaystyle \left( 8{ x }^{ 2 }-8{ y }^{ 2 } \right) \div 8={ x }^{ 2 }-{ y }^{ 2 }$$
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$$\displaystyle \left( 8{ x }^{ 2 }{ y }^{ 2 }-16xy \right) \div 8xy=\left( xy-2 \right) $$
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$$\displaystyle \left( { a }^{ 2 }bc+a{ b }^{ 2 }c+ab{ c }^{ 2 } \right) \div abc=\left( a+b+c \right) $$
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$$\displaystyle \left( { a }^{ 2 }bc+a{ b }^{ 2 }c+ab{ c }^{ 2 }+abc \right) \div abc=\left( a+b+c \right) $$
Explanation
$$\displaystyle \left( { a }^{ 2 }bc+a{ b }^{ 2 }c+ab{ c }^{ 2 }+abc \right) \div abc=\frac { { a }^{ 2 }bc+a{ b }^{ 2 }c+ab{ c }^{ 2 }+abc }{ abc } $$
$$\displaystyle =\frac { abc\left( a+b+c+1 \right) }{ abc } =a+b+c+1$$
$$\displaystyle \therefore \left( { a }^{ 2 }bc+a{ b }^{ 2 }c+ab{ c }^{ 2 }+abc \right) \div abc$$ is an incorrect statement.
Which of the following statements is correct?
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$$\displaystyle \left( 7{ x }^{ 2 }-7 \right) \div 7={ x }^{ 2 }-7$$
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$$\displaystyle \left( 5{ x }^{ 2 }+10 \right) \div 5={ x }^{ 2 }+10$$
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$$\displaystyle \left( 4{ x }^{ 2 }+12 \right) \div 2={ x }^{ 2 }+6$$
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$$\displaystyle \left( 6{ x }^{ 2 }+12 \right) \div 6={ x }^{ 2 }+2$$
Explanation
$$\displaystyle \left( 6{ x }^{ 2 }+12 \right) \div 6=\frac { 6{ x }^{ 2 }+12 }{ 6 }$$
$$=\dfrac { 6\left( { x }^{ 2 }+2 \right) }{ 6 } ={ x }^{ 2 }+2$$
$$\displaystyle \therefore \left( 6{ x }^{ 2 }+12 \right) \div 6$$ is a correct statement.
Factorise: $$\displaystyle -6{ a }^{ 2 }+6cb-6ca$$
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$$\displaystyle -6\left( { a }^{ 2 }+cb-ca \right) $$
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$$\displaystyle 6\left( { a }^{ 2 }-cb+ca \right) $$
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$$\displaystyle 6\left( { a }^{ 2 }+cb+ca \right) $$
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$$\displaystyle -6\left( { a }^{ 2 }-cb+ca \right) $$
Explanation
$$ -6{ a }^{ 2 }+6cb-6ca=\left( -6\times a\times a \right) +\left( 6\times c\times b \right) -\left( 6\times c\times a \right) $$
$$\displaystyle =-6( { a }^{ 2 }-cb+ca) $$
Factorise: $$\displaystyle 13{ x }^{ 2 }y-65x{ y }^{ 2 }$$
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0%
$$\displaystyle xy(x-y)$$
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$$\displaystyle 65xy(x-y)$$
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$$\displaystyle 13xy(x-5y)$$
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$$\displaystyle 13xy(x-y)$$
Explanation
$$\displaystyle 13{ x }^{ 2 }y-65x{ y }^{ 2 }=\left( 13\times x\times x\times y \right) -\left( 13\times y\times x\times y\times y \right) \\ $$
$$\displaystyle =13xy\left( x-5y \right) $$
Factorise: $$\displaystyle 5xy+15y$$
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0%
$$\displaystyle 5y(x+1)$$
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$$\displaystyle 5y(x+3)$$
0%
$$\displaystyle 5y(x+y)$$
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$$\displaystyle 5y(x+5)$$
Explanation
$$\displaystyle 5xy+15y=\left( 5\times x\times y \right) +\left( 5\times 3\times y \right) $$
$$\displaystyle =5y\left( x+3 \right) $$
Factorisation of the expression : $$\displaystyle -2{ x }^{ 2 }{ y }^{ 3 }+6{ x }^{ 3 }{ y }^{ 2 }-8{ x }^{ 2 }{ y }^{ 2 }$$ results in :
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$$\displaystyle -2{ x }^{ 2 }{ y }^{ 2 }\left( -y-3x-4 \right) $$
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$$-\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( y-3x+4 \right) $$
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$$\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( 3x+y-4 \right) $$
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$$\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( 3x-y+4 \right) $$
Explanation
$$\displaystyle -2{ x }^{ 2 }{ y }^{ 3 }+6{ x }^{ 3 }{ y }^{ 2 }-8{ x }^{ 2 }{ y }^{ 2 }$$
$$\displaystyle =\left[ (-2)\times { x }^{ 2 }\times { y }^{ 2 }\times y \right] +\left[ (-2) \times (-3)\times { x }^{ 2 }\times x\times { y }^{ 2 } \right] +\left[(-2) \times 4 \times { x }^{ 2 }\times { y }^{ 2 }\right]$$
$$\displaystyle =-2{ x }^{ 2 }{ y }^{ 2 }\left( y-3x+4 \right) $$
$$\displaystyle =-2{ x }^{ 2 }{ y }^{ 2 }\left( y-3x-4 \right) $$
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