a(b+c-a)^2+b(c+a-b)^2+c(a+b-c)^2+(b+c-a)(c+a-b)(a+b-c)
=a(b+c-a)^2+b(c+a-b)^2+c(a+b-c)^2+[c-(a-b)][c+(a-b)](a+b-c)
=a(b+c-a)^2+b(c+a-b)^2+c(a+b-c)^2+[c^2-(a-b)^2](a+b-c)
=a(b+c-a)^2+b(c+a-b)^2+(a+b-c)[c(a+b-c)+c^2-(a-b)^2]
=a(b+c-a)^2+b(c+a-b)^2+(a+b-c)[ac+bc+2ab-a^2-b^2]
=a(b+c-a)^2+b(c+a-b)^2+(a+b-c)[a(b+c-a)+b(c+a-b)]
=a(b+c-a)[(b+c-a)+(a+b-c)]+b(c+a-b)[(c+a-b)+(a+b-c)]
=a(b+c-a)*2b+b(c+a-b)*2a
=2ab[(b+c-a)+(c+a-b)]
=2ab*2c
=4abc