`x-[y-{z-(x-bar(y-z)}]=`

The expression x-[y-{z-(bar(x-y)}-(x+y)+z] when simplified reduces to

Simplify x - [ y - { z - (2x - bar(y+z)) }]

x+y-(z-x-[y+z-(x+y-{z+x-(y+z+x)})]) is equal to

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

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)]

Solve that |(y+z,x,x^(2)),(z+x,y,y^(2)),(x+y,z,z^(2))|=(x+y+z)(x-y)(y-z)(z-x)

Show that |(x, x^(2),y+z),(y,y^(2),z+x),(z,z^(2),x+y)| = (y-z)(z-x)(x-y)(x+y+z) .

Prove the following : |{:(x,x^(2),y+z),(y,y^(2),z+x),(z,z^(2),x+y):}|=(y-z)(z-x)(x-y)(x+y+z)

Using properties of determinants, prove that |{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)