如何证明（a+b+c)(ab+bc+ca)-abc=(a+b)(b+c)(c+a)

let f(a,b,c) =(a+b+c)(ab+bc+ca)-abc f(a,-a,c) =0=> a+b is a factor of f(a,b,c) f(a,b, -b)=0 =>b+c is a factor of f(a,b,c) f(-c,b, c)=0 => c+a is a factor of f(a,b,c) => (a+b+c)(ab+bc+ca)-abc=(a+b)(b+c)(c+a)