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

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

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

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

= (y + z)(  x 2  + yz + xy + xz) = (y + z)[( x 2  + xy) + (xz + yz)]

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

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)

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)

Ta co : 

Đặt tổng trên là A 

A= xy(x+y)+yz(y+z)+xz(x+z)+2xyz  

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

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

A= xy(x + y) + z(x + y + z)(y + x)  

A= (x + y)(xy + zx + zy + z² )   

A= (x + y)[x(y + z) + z(y + z)]  

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

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

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

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

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

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

\(=\left(x+z\right)\text{[}y\left(x+y\right)+z\left(x+y\right)\text{]}\)

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

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)

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)

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 ****.

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)

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 .-. )

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

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

\(=5x^2-18x-8=5x^2-20x+2x-8=5x\left(x-4\right)+2\left(x-4\right)=\left(5x+2\right)\left(x-4\right)\)

\(5=\left(x+y\right)\left(y+z\right)\left(z+x\right)\)