Question

Without actually calculating the cubes,find the value of 14^3-2^3-12^3

Answer 1

Answer: 3(14)(-2)(-12)=168×6=1008

Step-by-step explanation:

If (a+b+c)=0, then a^3+b^3+c^3=3abc

Answer 2

If a + b + c = 0, then

${a}^{3} + {b}^{3} + {c}^{3} = 3abc$

*Checking the above condition*

14 + (-2) + (-12)

= 14 - 2 - 12

= 14 - 14

= 0

Hence, it satisfies the above condition...

Therefore,

${ a}^{3} + {b}^{3} + {c}^{3} = 3abc$

= 3 (14) ( -12) ( -2)

= 1008