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