lean_workbook_plus_29400

for all real $x,y,z$ prove or disprove that \n\n $x^4+y^4+z^4+3(x^2y^2+x^2z^2+y^2z^2)\geq 2(x^3(y+z)+y^3(x+z)+z^3(x+y))$\n\nIt is a particular case of the more general inequality \n\n $\sum x^4+r(r+2)\sum y^2z^2 +(1-r^2)xyz\sum x \geq (r+1)\sum yz(y^2+z^2)$ , \n\nwhere $r$ is a real number.