Write the value of `|(x+y,y+z,z+x),(z,x,y),(-3,-3,-3)|`

Write the value of Delta=|{:(x+y,y+z,z+x),(z,x,y),(-3,-3,-3):}|

The value of |(x+y,y+z,z+x),(x,y,z),(x-y,y-z,z-x)|=

Write the value of Delta = |(x+y, y +z , z +x),(z, x,y),(-3,-3,-3)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

Find the value of x, y, z if [(x, y-z, z+3)]+[(y, 4, 3)]

Show that |(x+y,y+z,z+x),(y+z,z+x,x+y),(z+x,x+y,y+z)|=2[3xyz-x^(3)-y^(3)-z^(3)]

Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,y^2,y^3),(z,z^2,z^3)| = xyz(x-y(y-z)(z-x)

If x,y,z, are real and distinct number, then the value of ((x-y)^3+(y-z)^3+(z-x)^2)/((x-y)(y-z)(z-y)) is