How do I prove that (x+y) (x+z) (y+z) is greater or equal than 8xyz?

Answer 1

(x+y)(x+z)(y+z)=x^2y+x^2z+xzy+xz^2+y^2x+yxz+y^2z+yz^2

This is all I can do.

Answer 2

Compare the Arithmetic Mean and the Geometric means.