Q.14. 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

Solution:

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

 Let x = -12, y = 7 and z = 5

We see 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) (28)3 + (-15)3 + (-13)3

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

We see 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