Question

find the value without actually calculating (-2)³ + (-1)³ + (3)³

Answer 1

$( - 2) {}^{3} + ( - 1) + { - 3}^{3} \\ = ( - 8) + (- 1) + 27 \\ = (- 9 )+ 27 \\ = - 18$

Answer 2

_ANSWER_

$( - 2)^{3} + ( - 1)^{3} + {3}^{3} \\ \\ let \: x \: = \: - 2 \: \\ \\ y \: = \: - 1 \\ \\ z \: = \: 3 \\ \\ x + y + z \\ \\ = > \: - 2 - 1 + 3 = 0 \\ \\ we \: know \\ \\ if \: x + y + z = 0 \\ \\ then \\ \\ { x}^{3} + {y}^{3} + {z}^{3} = \: 3xyz \\ \\ { - 2}^{3} + { - 1}^{3} + {3}^{3} = \: 3( - 2)( - 1)(3) \\ \\ = \: 18 \: \: ans$

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