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1 tháng 11 2021

a) \(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right)\)

b) \(=2\left(x+y\right)-x\left(x+y\right)=\left(x+y\right)\left(2-x\right)\)

c) \(=3x\left(x-y\right)+5\left(x-y\right)=\left(x-y\right)\left(3x+5\right)\)

d) \(=\left(x+y\right)^2-25=\left(x+y-5\right)\left(x+y+5\right)\)

e) \(=x\left(x^2-11x+30\right)\)

f) \(=x\left(x-3\right)+6\left(x-3\right)=\left(x-3\right)\left(x+6\right)\)

8 tháng 9 2020

A = xy + y - 2x - 2

= y( x + 1 ) - 2( x + 1 )

= ( x + 1 )( y - 2 )

B = x2 - 3x + xy - 3y

= x( x - 3 ) + y( x - 3 )

= ( x - 3 )( x + y )

C = 3x2 - 3xy - 5x + 5y

= 3x( x - y ) - 5( x - y )

= ( x - y )( 3x - 5 )

D = xy + 1 + x + y

= y( x + 1 ) + ( x + 1 )

= ( x + 1 )( y + 1 )

E = ax - bx + ab - x2

= ( ax - x2 ) + ( ab - bx )

= x( a - x ) + b( a - x )

= ( a - x )( x + b )

F = x2 + ab + ax + bx

= ( ax + x2 ) + ( ab + bx )

= x( a + x ) + b( a + x )

= ( a + x )( x + b )

G = a3 - a2x - ay + xy

= a2( a - x ) - y( a - x )

= ( a - x )( a2 - y )

Bonus : = ( a - x )[ a2 - ( √y )2 ]

             = ( a - x )( a - √y )( a + √y )

H = 2xy + 3z + 6y + xz

= ( 6y + 2xy ) + ( 3z + xz )

= 2y( 3 + x ) + z( 3 + x )

= ( 3 + x )( 2y + z )

8 tháng 9 2020

A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1

B = x2 - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)

C = 3x2 - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)

D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)

E = ax - bx + ab - x2 = ax - x2 + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)

F = x2 + ab + ax + bx = ab + ax + bx + x2 = a(b + x) + x(b + x) = (a + x)(b + x)

G = a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)

H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)

9 tháng 7 2016

1)\(x^4+2x^3+x^2\)

=\(\left(x^4+x^3\right)+\left(x^3+x^2\right)\)đật nhân tử chung ra

=\(x^2\left(x+1\right)^2\)

2) pt => \(\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)

=\(\left(x+y\right)^3-\left(x+y\right)\)

=\(\left(x+y\right)\left(\left(x+y\right)^2+1\right)\)

3)chia tất cả cho 5 pt => \(x^2-2xy+y^2-4x^2\)

=\(\left(x+y\right)^2-4z^2\)

=\(\left(x+y+2z\right)\left(x+y-2z\right)\)

4)pt => \(2\left(x-y\right)-\left(x^2-2xy+y^2\right)\)

=\(2\left(x-y\right)-\left(x-y\right)^2\)

=\(\left(x-y\right)\left(2-x+y\right)\)

k chi nha

12 tháng 7 2019

a,\(xy+3x-7y-21\)

\(=x\left(y+3\right)-7\left(y+3\right)\)

\(=\left(y+3\right)\left(x-7\right)\)

12 tháng 7 2019

\(b,2xy-15-6x+5y\)

\(=\left(2xy-6x\right)+\left(-15+5y\right)\)

\(=2x\left(y-3\right)-5\left(3-y\right)\)

\(=2x\left(y-3\right)+5\left(y-3\right)\)

\(=\left(y-3\right)\left(2x+5\right)\)

14 tháng 8 2015

a/ \(=3y^2-6y-2x+1\)

b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)

c/ \(=\left(2-x\right)^3\)

d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)

\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)

\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)

e/ \(=xy-x^2+2x-y^2+xy-2y\)

\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)

14 tháng 8 2015

a) =(2x+3y-1)2

b)=-(x-1)3

c)=-(x3-6x2+12x-8)=-(x-2)3

d)x3 + 2x2y + xy2 – 9x

    = x(x2 + 2xy + y2 -9)

    = x[(x2 + 2xy + y2) - 32]

    = x[(x + y)2 - 32]

    = x (x + y – 3)(x + y + 3)

e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)

20 tháng 7 2017

a) \(2x^3+6x=2x\left(x^2+3\right)\)

\(\Leftrightarrow2x^3+6x=2x^3+6x\)

\(\Leftrightarrow0x=0\)

b) \(5x\left(x-2\right)-3x^2\left(x-2\right)=x\left(x-2\right)\left(5-3x\right)\)

c) \(3x\left(x-5y\right)-2y\left(5y-x\right)=\left(x-5y\right)\left(3x+2y\right)\)

e) \(2ax^3+4bx^2y+2x^2\left(ax-by\right)=2x^2\left(ax+2by\right)+2x^2\left(ax-2by\right)\)

\(=2x^2\left(ax+2by+ax-2by\right)=4ax^3\)

f) \(3x^2\left(y^2-2x\right)-15x\left(2x-y\right)^2=-3x\left(2x-y^2\right)\left(x+5\right)\)

16 tháng 11 2018

b.10x(x-y)-6y(y-x)=10x(x-y)+6y(x-y)=(10x+6y)(x-y)

16 tháng 11 2018

c.3x2+5y-3xy-5x=(3x2--3xy)-(5x-5y)=3x(x-y)-5(x-y)=(3x-5)(x-y)

12 tháng 9 2020

Áp dụng HĐT a2 - b2 = ( a - b )( a + b )

và tính chất an.bn = ( a.b )n ( với n ∈ N* )

a) ( 3x + 1 )2 - ( x + 1 )2

= [ ( 3x + 1 ) - ( x + 1 ) ][ ( 3x + 1 ) + ( x + 1 ) ]

= ( 3x + 1 - x - 1 )( 3x + 1 + x + 1 )

= 2x( 4x + 2 )

= 2x.2( 2x + 1 )

= 4x( 2x + 1 )

b) ( x + y )2 - ( x - y )2

= [ ( x + y ) - ( x - y ) ][ ( x + y ) + ( x - y ) ]

= ( x + y - x + y )( x + y + x - y )

= 2y.2x = 4xy

c) ( 2xy + 1 )2 - ( 2x + y )2

= [ ( 2xy + 1 ) - ( 2x + y ) ][ ( 2xy + 1 ) + ( 2x + y ) ]

= ( 2xy + 1 - 2x - y )( 2xy + 1 + 2x + y )

= [ ( 2xy - 2x ) - ( y - 1 ) ][ ( 2xy + 2x ) + ( y + 1 ) ]

= [ 2x( y - 1 ) - ( y - 1 ) ][ 2x( y + 1 ) + ( y + 1 ) ]

= ( y - 1 )( 2x - 1 )9 y + 1 )( 2x + 1 )

d) 9( x - y )2 - 4( x + y )2

= 32( x - y )2 - 22( x + y )2 

= [ 3( x - y ) ]2 - [ 2( x + y ) ]2

= ( 3x - 3y )2 - ( 2x + 2y )2

= [ ( 3x - 3y ) - ( 2x + 2y ) ][ ( 3x - 3y ) + ( 2x + 2y ) ]

= ( 3x - 3y - 2x - 2y )( 3x - 3y + 2x + 2y ) 

= ( x - 5y )( 5x - y )

e) ( 3x - 2y )2 - ( 2x - 3y )2

= [ ( 3x - 2y ) - ( 2x - 3y ) ][ ( 3x - 2y ) + ( 2x - 3y ) ]

= ( 3x - 2y - 2x + 3y )( 3x - 2y + 2x - 3y )

= ( x + y )( 5x - 5y )

= ( x + y )5( x - y )

f) ( 4x2 - 4x + 1 ) - ( x + 1 )2

= ( 2x - 1 )2 - ( x + 1 )2

= [ ( 2x - 1 ) - ( x + 1 ) ][ ( 2x - 1 ) + ( x + 1 ) ]

= ( 2x - 1 - x - 1 )( 2x - 1 + x + 1 )

= 3x( x - 2 )