14.Without actually calculating the cubes, find the value of each of the following :
i)$$(-12)^3 + (5)^3 + (7))^3$$
ii)$$(28)^3 + (-15)^3 + (-13)^3$$
$$x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)$$
Also, if x + y + z = 0 then, $$x^3 + y^3 + z^3 = 3xyz$$
So, $$(-12)^3 + (5)^3 + (7))^3 = 3(-12)(7)(5)$$
$$= -1260$$
So, $$(28)^3 + (-15)^3 + (-13))^3 = 3(-13)(28)(-15)$$
$$= 16380$$