solve `|[y+z, x, x] , [y, z+x, y] , [z, z, x+y]|`

|[z+y,x,x] , [y,z+x,y] , [z,z,x+y]|=

Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

Prove that |[x+y, y+z, z+x] , [z+x, x+y, y+z] , [y+z, z+x, x+y]|=2|[x,y,z] , [z,x,y] , [y,z,x]|

|[y+z, x, y],[z+x, z, x],[x+y, y, z]|=...

Show that abs([y+z ,x,x],[y,z+x,y],[z,z,x+y])=4xyz

show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)