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5 tháng 10 2015

a) 

5x-5y+ax-ay = 5(x-y) +a(x-y) = (x-y)(5+a)

b) a^3 -a^2x-ay+xy = a^2(a-x) -y(a-x) = (a-x)(a^2-y)

c) xy(x+y) +yz(y+z) +xz(x+z) +2xyz = x^2.y+xy^2 +y^2.z+xz^2 +x^2.z+xz^2 +2xyz

= (x^2.y+x^2.z)+(xy^2+xz^2+2xyz)+(y^2.z+yz^2) = x^2(y+z) +x.(y+z)^2 +yz(y+z)

=(y+z)(x^2+x+yz)

28 tháng 7 2017

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

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

3 ) \(5x-5y+ax-ay=5.\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(5+a\right)\)

4 ) \(a^3-a^2x-ay+xy=a^2.\left(a-x\right)-y.\left(a-x\right)=\left(a-x\right)\left(a^2-y\right)\)

5 ) \(xy.\left(x+y\right)+yz.\left(y+z\right)+xz.\left(x+z\right)+2xyz\)

\(=xy.\left(x+y\right)+y^2z+yz^2+x^2z+xz^2+xyz+xyz\)

\(=xy.\left(x+y\right)+\left(y^2z+xyz\right)+\left(yz^2+xz^2\right)+\left(x^2z+xyz\right)\)

\(=xy.\left(x+y\right)+yz.\left(x+y\right)+z^2.\left(x+y\right)+xz.\left(x+y\right)\)

\(=\left(x+y\right)\left(xy+yz+z^2+xz\right)=\left(x+y\right)\left[\left(xy+xz\right)+\left(yz+z^2\right)\right]\)

\(=\left(x+y\right)\left[x.\left(y+z\right)+z.\left(y+z\right)\right]=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)

chỗ nào k hiểu hỏi mình lại ớ 

\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)

\(=xy\left(x+y\right)+xyz+xz\left(x+z\right)+xyz+yz\left(y+z\right)\)

\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(y+z\right)\)

\(=x\left(y+z\right)\left(x+y+z\right)+yz\left(y+z\right)\)

\(=x\left(y+z\right)\left(x+y+z+yz\right)\)

 

15 tháng 6 2017

a) \(5x-5y+ax-ay\)

\(\Leftrightarrow\) \(\left(5x+ax\right)-\left(5y+ay\right)\)

\(\Leftrightarrow\) \(x\left(5+a\right)-y\left(5+a\right)\)

\(\Leftrightarrow\) \(\left(5+a\right)\left(x-y\right)\)

15 tháng 6 2017

b) \(a^3-a^2x-ay+xy\)

\(\Leftrightarrow\) \(a^2\left(a-x\right)-y\left(a-x\right)\)

\(\Leftrightarrow\) \(\left(a-x\right)\left(a^2-y\right)\)

8 tháng 12 2015

xy(x+y)+yz(y+z)+xz(x+z)+2xyz 

= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 

= xy(x + y) + yz(y + z + x) + xz(x + z + y) 

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

= (x + y)(y + z)(z + x)

14 tháng 10 2020

1) \(4x^2-7x-2=4x^2-8x+x-2=\left(4x^2-8x\right)+\left(x-2\right)\)

\(=4x\left(x-2\right)+\left(x-2\right)=\left(x-2\right)\left(4x+1\right)\)

2) \(4x^2+5x-6=4x^2+8x-3x-6=\left(4x^2+8x\right)-\left(3x+6\right)\)

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

3) \(5x^2-18x-8=5x^2-20x+2x-8=\left(5x^2-20x\right)+\left(2x-8\right)\)

\(=5x\left(x-4\right)+2\left(x-4\right)=\left(x-4\right)\left(5x+2\right)\)

4) \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)

\(=xy\left(x+y\right)-y^2z-yz^2+x^2z-xz^2\)

\(=xy\left(x+y\right)+\left(x^2z-y^2z\right)-\left(yz^2+xz^2\right)\)

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

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

\(=xy\left(x+y\right)+\left(zx-zy\right)\left(x+y\right)-z^2\left(x+y\right)\)

\(=\left(x+y\right)\left(xy+xz-yz-z^2\right)=\left(x+y\right).\left[x\left(y+z\right)-z\left(y+z\right)\right]\)

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

14 tháng 10 2020

1) 4x2 - 7x - 2 = 4x2 - 8x + x - 2 = 4x( x - 2 ) + ( x - 2 ) = ( x - 2 )( 4x + 1 )

2) 4x2 + 5x - 6 = 4x2 - 8x + 3x - 6 = 4x( x - 2 ) + 3( x - 2 ) = ( x - 2 )( 4x + 3 )

3) 5x2 - 18x - 8 = 5x2 - 20x + 2x - 8 = 5x( x - 4 ) + 2( x - 4 ) = ( x - 4 )( 5x + 2 )

4) xy( x + y ) - yz( y + z ) + xz( x - z )

= x2y + xy2 - y2z - yz2 + xz( x - z )

= ( x2y - yz2 ) + ( xy2 - y2z ) + xz( x - z )

= y( x2 - z2 ) + y2( x - z ) + xz( x - z )

= y( x - z )( x + z ) + y2( x - z ) + xz( x - z )

= ( x - z )[ y( x + z ) + y2 + xz ]

= ( x - z )( xy + yz + y2 + xz )

= ( x - z )[ ( xy + y2 ) + ( xz + yz ) ]

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

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

5) xy( x + y ) + yz + xz( x + z ) + 2xyz ( đề có thiếu không vậy .-. )

28 tháng 9 2016

xy(x+y)+yz(y+z)+xz(x+z)+2xyz 
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 
= xy(x + y) + yz(y + z + x) + xz(x + z + y) 
= xy(x + y) + z(x + y + z)(y + x) 
= (x + y)(xy + zx + zy + z2
= (x + y)[x(y + z) + z(y + z)] 
= (x + y)(y + z)(z + x)

28 tháng 9 2016

xy(x+y)+yz(y+z)+xz(x+z)+2xyz 
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 

= xy(x + y) + yz(y + z + x) + xz(x + z + y) 

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

= (x + y)(y + z)(z + x)

30 tháng 9 2015

nhu the nay:

   ( xy( x + y )+ xyz )+( yz( y + z )+ xyz )+( xz( a +c )+ xyz)

= xy( x+y+z )+ yz( x + y + z )+ xz( x + y + z )

= ( x + y + z)( xy + yz +zx )

xong rui do dung thi ****.

24 tháng 7 2016

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

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

2)\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(a+5\right)\)

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

28 tháng 7 2016

xy(x+y)+yz(y+z)+xz(x+z)+2xyz 

= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 

= xy(x + y) + yz(y + z + x) + xz(x + z + y) 

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

= (x + y)(y + z)(z + x)

28 tháng 7 2016

xy(x+y)+yz(y+z)+xz(x+z)+2xyz 

= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 

= xy(x + y) + yz(y + z + x) + xz(x + z + y) 

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

= (x + y)(y + z)(z + x)