Question
Evaluate:
$(28)^3 + (-15)^3 + (-13)^3$
$(28)^3 + (-15)^3 + (-13)^3$
✓
Answer
$(28)^3 + (-15)^3 + (-13)^3$
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, $x = (-28), y = -15, z = -13$
$(28)^3 + (-15)^3 + (-13)^3$
$= (28 - 15 - 13)[(28)^2 + (-15)^2 + (-13)^2 - 28(-15) - (-15)(-13) - 28(-13)] + 3 \times 28(-15)(-13)$
$= 0 + 16380$
$= 16380$
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, $x = (-28), y = -15, z = -13$
$(28)^3 + (-15)^3 + (-13)^3$
$= (28 - 15 - 13)[(28)^2 + (-15)^2 + (-13)^2 - 28(-15) - (-15)(-13) - 28(-13)] + 3 \times 28(-15)(-13)$
$= 0 + 16380$
$= 16380$
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