" 13."a^(3)(b-c)^(3)+b^(3)(c-a)^(3)+c^(3)(a-b)^(3)

Factorize: a^3(b-c)^3+b^3(c-a)^3+c^3(a-b)^3

Factorize a(b^(3)-c^(3))+b(c^(3)-a^(3))+c(a^(3)-b^(3))

What is the value of the expression ? ((a-b)^(3)+(b-c)^(3)+(c-a)^(3))/(3(a-b)(b-c)(c-a))=?

Prove that ((a^(2)-b^(2))^(3)+(b^(2)-c^(2))^(3)+(c^(2)-a^(2))^(3))/((a-b)^(3)+(b-c)^(3)+(c-a)^(3))=(a+b)(b+c)(c+a)

the value of the determinant |(0, b^(3)-a^(3),c^(3)-a^(3)),(a^(3)-b^(3),0,c^(3)-b^(3)),(a^(3)-c^(3),b^(3)-c^(3),0)| is equal to -

(a-b)^3+(b-c)^3+(c-a)^3