Factorise : `x(y-z)^(2)+y(z-x)^(2)+z(x-y)^(2)+8xyz`

Factorise : x(1+y^(2))(1+z^(2))+y(1+z^(2))(1+x^(2))+z(1+x^(2))(1+y^(2))+4xyz

Factorise : (x+y+z)(x^(3)+y^(3)+z^(3)+xyz)-x^(4)-y^(4)-z^(4)

Resolve into factors x(y^2+z^2)-y(z^2+x^2)-z(x^2+y^2)+2xyz

(a) Factorise : x^(2) - (z-5)x - 5z (b) Factorise : x^(2) + x - y + y^(2) - 2xy

Factorise 4x^2+y^2+z^2-4x y-2y z+4x z .

If x + y + z = xyz , prove that x(1 -y^(2)) (1- z^(2))+ y(1- z^(2))(1- x^(2)) +z(1-x^(2)) (1- y^(2)) = 4xyz .

If x+y+z=xzy , prove that : x(1-y^2) (1-z^2) + y(1-z^2) (1-x^2) + z (1-x^2) (1-y^2) = 4xyz .

If x+y+z=xzy , prove that : x(1-y^2) (1-z^2) + y(1-z^2) (1-x^2) + z (1-x^2) (1-y^2) = 4xyz .