Question

14. Without actually calculating the cubes, find the value of each of the following ( (-12)+(7) +(5) (m) (28)+(-15)+(-13)​

Answer 1

Step-by-step explanation:

(-12)³ + (7)³ + (5)³

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

Then x + y + z = -12 + 7 + 5 = 0

We know the algebraic identity, if x + y + z = 0 then x³ + y³ + z³ = 3xyz

Thus, (-12)³ + (7)³ + (5)³ = 3(-12)(7)(5)

= -1260

(28)³ + (-15)³ + (-13)³

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

Then x + y + z = 28 - 15 - 13 = 0

We know the algebraic identity, if x + y + z = 0 then x³ + y³ + z³ = 3xyz

Thus, (28)³ + (-15)³ + (-13)³ = 3(28)(-15)(-13)

= 16380

Ans -1260

16380