Question

Without actually calculating the cubes, find the value of each of the following:

(i) (-12)3 + (7)3 + (5)3

(ii) (28)3 + (-15)3 + (-13)3

Answer 1

(i) (-12)3 + (7)3 + (5)3

Let -12 = x, 7 = y, 5 = z, then

x3 + y3 + z3 = 3xyz.

∴ (-12)3 + (7)3 + (5)3

= 3(-12)(7)(5)

= -36 × 35

= -1260.

(ii) (28)3 + (-15)3 + (-13)3

Let x = 28, y = -15, z = -13, then

x3 + y3 + z3 = 3xyz

∴ (28)3 + (-15)3 + (-13)3

= 3(28)(- 15)(-13)

= 84 × 195

= 16380