Without actually calculating the cubes, find the value of each of the following:
(i) 
(ii) 
(i) Let x = -12, y = 7 and z = 5
We observed that,
x + y + z = -12 + 7 + 5 = 0
We know that if,
x + y + z = 0
Then,
x3 + y3 + z3 = 3xyz
(-12)3 + (7)3 + (5)3 = 3 (-12) (7) (5)
= -1260
(ii) Let x = 28, y = -15 and z = -13
We observed that,
x + y + z = 28 – 15 – 13 = 0
We know that if,
x + y + z = 0
Then,
x3 + y3 + z3 = 3xyz
(28)3 + (-15)3 + (-13)3 = 3 (28) (-15) (-13)
= 16380
30