a^2b-ab^2+a^c-ac^2-3abc+b^2c+bc^2

a^2b-ab^2+a^2c-ac^2-3abc+b^2c+bc^2
=(a^2b-ab^2-abc)+(a^2c-ac^2-abc)+(b^2c+bc^2-abc)
=ab(a-b-c)+ac(a-c-b)+bc(b+c-a)
=ab(a-b-c)+ac(a-b-c)-bc(a-b-c)
=(ab+ac-bc)(a-b-c)