Question

2X + Y+ Z = 0 THEN FIND THE VALUE OF 8X CUBE + Y CUBE + Z CUBE

Answer 1

Use the following identity:

${(a + b + c)}^{3} \\ = ( {a}^{3} + {b}^{3} + {c}^{3} ) + 3((a + b + c)(ab + bc + ac) - abc)$
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$2x + y + z = 0$

$8 {x}^{3} + {y}^{3} + {z}^{3} \\ \\ = {(2x)}^{3} + {y}^{3} + {z}^{3}$

$= {(2x+ y+ z)}^{3} - 3((2x + y + z)(2xy + yz + 2xz) - 2xyz) \\ \\ = {0}^{3} - 3((0) \times (2xy + yz + 2xz) - 2xyz)$

$= - 3(0 - 2xyz) \\ \\ = 6xyz$

Answer 2

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