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

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

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

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

\(\text{Chúc bạn học tốt \!}\)

\(\text{Nếu đúng thì tích nha !}\)

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

=x²y+xy²+y²x+yz²+x²z+xz²+2xyz

=> hết biết làm

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(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)

**** đi nak , làm rui đó

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)

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

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

ko tick cau tra loi cho nguoi ta mot lan a ?

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

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

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

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

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

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

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