Question

tính: \(\left(x+y-z\right)^2-\left(x+y+z\right)^2\)

Answer 1

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

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

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

\(=-4xz-4yz\)

\(=-4\left(xz+yz\right)\)

Answer 2

Cách khác :3

\(\left(x+y-z\right)^2-\left(x+y+z\right)^2=\left(x+y-z+x+y+z\right)\left(x+y-z-x-y-z\right)=-2z\left(2x+2y\right)=-4z\left(x+y\right)\)