$1.$
$c) a(b^3−c^3)+b(c^3−a^3)+c(a^3−b^3)$
$= a(b^3 - c^3) - b(a^3 - c^3) + c(a^3 - b^3)$
$= a(b^3 - c^3) - b[(a^3 - b^3) + (b^3 - c^3)] + c(a^3 - b^3)$
$= a(b^3 - c^3) - b(a^3 - b^3) - b(b^3 - c^3) + c(a^3 - b^3)$
$= (b^3 - c^3)(a - b) - (a^3 - b^3)(b - c)$
$= (b - c)(b^2 + bc + c^2)(a - b) -...