Prove that \[\frac{1}{(2-\sqrt{3})^3}+\frac{1}{(2+\sqrt{3})^3}=52.\]

Show that \((a-b)\) is a factor of \[a^3(b-c)+b^3(c-a)+c^3(a-b)\] and hence factorise the expression completely.

Prove that \[\frac{1}{(2-\sqrt{3})^3}+\frac{1}{(2+\sqrt{3})^3}=52.\]

Show that \((a-b)\) is a factor of \[a^3(b-c)+b^3(c-a)+c^3(a-b)\] and hence factorise the expression completely.