simplify: i) a^3(b-c)+b^3(c-a)+c^3(a-b)?

Question

ii) a(b^4-c^4)+b(c^4-a^4)+c(a^4-b^4)
iii) (x+y+z)(xy+yz+zx)-xyz

Answer 1

1) you get ba^3 - ca^3 + cb^3 - ab^3 + ac^3 - bc^3 =0
2) likewise 0
3) messy
x²y + xyz + x²z + xy² + y²z + xyz + xyz + yz² + xz² - xyz =
x²y + x²z + xy² + y²z + yz² + xz² + 2xyz