\(\left(x+y-z\right)^2-\left(x+y+z\right)^2\)
\(=\left(x^2+y^2+z^2+2xy-2xz-2yz\right)-\left(x^2+y^2+z^2+2xy+2xz+2yz\right)\)
\(=x^2+y^2+z^2+2xy-2xz-2yz-x^2-y^2-z^2-2xy-2xz-2yz\)
\(=-4xz-4yz\)
\(=-4\left(xz+yz\right)\)
Cách khác :3
\(\left(x+y-z\right)^2-\left(x+y+z\right)^2=\left(x+y-z+x+y+z\right)\left(x+y-z-x-y-z\right)=-2z\left(2x+2y\right)=-4z\left(x+y\right)\)