a^2(b-c)+b^2(c-a)+c^2(a-b)

a^2(b-c)+b^2(c-a)+c^2(a-b)
=a^2(b-c)+b^2c-ab^2+ac^2-bc^2
=a^2(b-c)+a(c^2-b^2)+cb(b-c)
=a^2(b-c)+a(c-b)(c+b)+cb(b-c)
=(b-c)(a^2-ac-ab+cb)
=(b-c)[a(a-c)-b(a-c)]
=(b-c)(a-c)(a-b)
(a-4)^2+(b-4)^2+2(ab-8)
=a^2-8a+16+b^2-8b+16+2ab-16
=[a^2+2ab+b^2]-8(a+b)+16
=(a+b)^2-8(a+b)+16
=(a+b-4)^2
2(a^2+b^2)(a+b)^2-(a^2-b^2)^2
=2(a^2+b^2)(a+b)^2-(a-b)^2(a+b)^2
=(a+b)^2[2(a^2+b^2)-(a-b)^2]
=(a+b)^2[2a^2+2b^2-a^2-b^2+2ab]
=(a+b)^2(a+b)^2
=(a+b)^4