>>770
a^2(b-c)+b^2c-ab^2+ac^2-bc^2
=a^2(b-c)+bc(b-c)-a(b^2-c^2)
=(a^2+bc)(b-c)-a(b+c)(b-c)
=(a^2-ab+bc-ca)(b-c)
=(a(a-b)-c(a-b))(b-c)
=-(a-b)(b-c)(c-a)