Question

Without actually calculating the cubes, find the value of the following:- (28)³ + (–15)³ + (–13)³

Answer 1

(28)³ + (–15)³ + (–13)³ 

Let x = 28, y = −15, and z = −13

It can be observed that,

x + y + z = 28 + (−15) + (−13) = 28 − 28 = 0

It is known that if x + y + z = 0, then

x³ + y³ + z³ = 3xyz

∴ (28)³ + (–15)³ + (–13)³ = 3(28)(-15)(-13) = 16380