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14.Without actually calculating the cubes, find the value of each of the following :
i)\((-12)^3 + (5)^3 + (7))^3\)
ii)\((28)^3 + (-15)^3 + (-13)^3\)
Answer :

We know that,
\(x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)\)
Also, if x + y + z = 0 then, \(x^3 + y^3 + z^3 = 3xyz\)

i)Here, -12 + 7 + 5 = 0
So, \((-12)^3 + (5)^3 + (7))^3 = 3(-12)(7)(5)\)
\(= -1260\)

ii)Here, 28 - 15 - 13 = 0
So, \((28)^3 + (-15)^3 + (-13))^3 = 3(-13)(28)(-15)\)
\(= 16380\)