Without actually calculating the cubes, find the value of the following: ${(- 12)}^{3}$ + ${(7)}^{3}$ + ${(5)}^{3}$

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Solution

${(- 12)}^{3}$ + ${(7)}^{3}$ + ${(5)}^{3}$

$∵$ (-12) + (7) + (5) = 0

Using identity, if x + y + z = 0, then $x^{3}$ + $y^{3}$ + $z^{3}$ = 3xyz.

= 3 × (-12)× (7)× (5) = -1260 ...(answer)

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