kết quả 3*(y+x)*(z+x)*(z+y)

ta có :

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

\(=x^3+y^3+z^3+3yz\left(y+z\right)+3x\left(y+z\right)\left(x+y+z\right)\)

Vậy \(\left(x+y+z\right)^3-x^3-y^3-z^3=3yz\left(y+z\right)+3x\left(y+z\right)\left(x+y+z\right)=3\left(y+z\right)\left(x^2+xy+xz+yz\right)\)\(=3\left(x+y\right)\left(x+z\right)\left(y+z\right)\)

x² + 2xz + 2xy + 4yz

= ( x² + 2xy ) + ( 2xz +4yz )

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

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

2xy + 3z +6y + xz

= 2xy + 6y + xz + 3z

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

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

2xy+3z+6y+xz

=2xy+6y+xz+3z

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

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

x^2-2xy+tx-2ty 

=(x^2-2xy)+(tx-2ty )

=x.(x-2y)+t.(x-2y)

=(x-2y).(x+t)

\(x^2-2xy+tx-2ty\)   

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

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

\(\frac{a^2}{\left(a-b\right)\left(a-c\right)}+\frac{b^2}{\left(b-a\right)\left(b-c\right)}+\frac{c^2}{\left(c-a\right)\left(c-b\right)}\)

\(=-\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)

\(=-\frac{a^2b-a^2c+b^2c-b^2a+c^2\left(a-b\right)}{\left(a-b\right)\left(b-c\right)\left(b-a\right)}\)

\(=-\frac{-c\left(a^2-b^2\right)+ab\left(a-b\right)+c^2\left(a-b\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}=-\frac{\left(a-b\right)\left[-c\left(a+b\right)+ab+c^2\right]}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)

\(=-\frac{\left(a-b\right)\left(-ac-bc+ab+c^2\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}=\frac{-\left(a-b\right)\left[-b\left(c-a\right)+c\left(c-a\right)\right]}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)

\(=-\frac{\left(a-b\right)\left(c-a\right)\left(-b+c\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}=\frac{\left(a-b\right)\left(c-a\right)\left(b-c\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}=1\)

x²-2xy+y²-xz+yz

=(x²-2xy+y²)-(xz-yz)

=(x-y)²-z(x-y)

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

HT

x² -2xy + y² -xz +yz

= ( x-y)² - ( xz -yz )

= ( x -y )² -z( x -y )

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

* Sxl

????? 

?????

x² - y² + 2yz - z²

= x² - ( y² -2yz + z² )

= x² - ( y-z )²

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

x² - y² + 2yz - z²

= x² - ( y² - 2yz + z² )

= x² - ( y - z )²

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

x² - 6xy - 25z² + 9y²

= ( x² - 6xy + 9y² ) - 25z²

= ( x - 3y ) ² - ( 5z)²

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

x² - 6xy - 25z² + 9y²

= ( x² - 6xy + 9y² ) - 25z²

= ( x - 3y )² - ( 5z )²

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

#TNQ

3x² - 6xy + 3y² - 12z² 

 = 3(x² - 2xy + y² - 4z²) 

= 3[(x - y)²  - (2z)²]

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