`4x(x+y)(x+z).(x+y+z)+y^2z^2`

`=4[(x+y)(x+z)][x(x+y+z)]+(yz)^2`

`=4(x^2+xy+xz+yz)(x^2+xy+xz)+(yz)^2`

`=4(x^2+xy+xz)^2+4(x^2+xy+xz)yz+(yz)^2`

`=[2(x^2+xy+xz)]^2+4(x^2+xy+xz)yz+(yz)^2`

`=[2(x^2+xy+xz)+yz]^2`

`=(2x^2+2xy+2xz+yz)^2`