Question
Evaluate: $(-12)^3 + 7^3 + 5^3$
✓
Answer
$(-12)^3 + 7^3 + 5^3$
We know: $x^3 + y^3 + z^3 - 3xyz$
$= (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) x^3 + y^3 + z^3$
$= (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) + 3xyz$
Here,$ x = (-12), y = 7, z$
$= 5 (-12)^3 + 7^3 + 5^3$
$= (-12 + 7 + 5)[(-12)^2 + 7^2 + 5^2 - 7(-12) - 35 + 60] + 3(-12) \times 35$
$= 0 - 1260$
$= -1260$
We know: $x^3 + y^3 + z^3 - 3xyz$
$= (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) x^3 + y^3 + z^3$
$= (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) + 3xyz$
Here,$ x = (-12), y = 7, z$
$= 5 (-12)^3 + 7^3 + 5^3$
$= (-12 + 7 + 5)[(-12)^2 + 7^2 + 5^2 - 7(-12) - 35 + 60] + 3(-12) \times 35$
$= 0 - 1260$
$= -1260$
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