Question
Without actually calculating the cube, find the value of $(-12)^3+(7)^3+(5)^3$.
✓
Answer
$a^3+b^3+c^3=3 a b c$
$\text { If } a+b+c=0$
Given: $a=-12, b=7, c=5$
And $a+b+c=-12+7+5=0$
Then,
$(-12)^3+(7)^3+(5)^3=3 \times-12 \times 7 \times 5$
$=-1260$
$\text { If } a+b+c=0$
Given: $a=-12, b=7, c=5$
And $a+b+c=-12+7+5=0$
Then,
$(-12)^3+(7)^3+(5)^3=3 \times-12 \times 7 \times 5$
$=-1260$
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