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