" Show that "|[y+z,x,x],[y,z+x,y],[z,z,x+y]|=4xyz

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

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

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

Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

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

By using properties of determinants. Show that: |[x,x^2,y z],[ y, y^2,z x],[ z, z^2,x y]|=(x-y)(y-z)(z-x)(x y+y z+z x)

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

|[y+z, x, x] , [y, z+x, y] , [z, z, x+y]|= (i) x^2y^2z^2 (ii) 4x^2y^2z^2 (iii) xyz (iv) 4xyz

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