Надо разложить на множители выражение х((у+z) в квадрате) + y((x+z) в квадрате) + z((x+y) в квадрате) - 4xyz

х(у+z)²+ y(x+z)² + z(x+y)² - 4xyz=
=х(у+z)²+ y(x+z)² + z(x²+2xy+y²) - 4xyz=
=х(у+z)²+ y(x+z)² + z(x²-2xy+y²) =
=х(у+z)²+ y(x+z)² + z(x-y)² =
=х(у+z)²+ y(x-y+y+z)² + z(x-y)² =
=х(у+z)²+ y(x-y)²+2y(x-y)(y+z)+y(y+z)² + z(x-y)² =(y+z)²(x+y)+(x-y)²(y+z)+2y(x-y)(y+z)=
=(y+z)·((y+z)(x+y)+(x-y)²+2y(x-y))=(y+z)·((y+z)(x+y)+(x-y)(x-y+2y))=
(y+z)·((y+z)(x+y)+(x-y)(x+y))=(y+z)(x+y)(y+z+x-y)=(y+z)(x+y)(z+x)