If $x + y + 2 = 0$ then find the value of $x^{3} + y^{3} + 8$ .

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Solution

Given that;
$x + y + 2 = 0 \dots (1)$
To find:
$x^{3} + y^{3} + 8 = ?$
Taking cube on both sides of $(1)$ :
$(x + y + 2)^{3} = 0$
$x^{3} + y^{3} + 8 (x + y + 2) (x y + 2 y + 2 x) = 0.$
$x^{3} + y^{3} + 8 + (0) (x y + 2 y + 2 x) = 0$
$x^{3} + y^{3} + 8 = 0$

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