Verified answer

x(y² - z²) + y(z² - x²) + z(x² - y²) = x·y²-x·z²+y·z²-y·x²+z·x²-z·y² =

= (yz² - xz²) + (x²z - y²z) + (xy² - x²y) = z²(y - x) + z(x² - y²) + xy(y - x) =

= z²(y - x) - z(y - x)(x + y) + xy(y - x) = (y - x)(z² - zx - zy + xy) =

= (y - x)[(z² - zx) - (zy - xy)] = (y - x) [z(z - x) - y(z - x)] = (y - x)(z - x)(z - y)