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