Evaluate:

\( 48^{3}-30^{3}-18^{3} \)

Given: 

\( 48^{3}-30^{3}-18^{3} \)

To do: 

We have to evaluate the given expression.

Solution: 

We know that,

If $x+y+z=0$, then $x^{3}+y^{3}+z^{3}=3 x y z$.

Let $a=48, b=-30$ and $c=-18$

$a+b+c=48-30-18=0$

This implies,

$a^{3}+b^{3}+c^{3}=3 a b c$

$48^{3}-30^{3}-18^{3}=3 \times 48 \times(-30) \times (-18)$

$=3 \times 48 \times 30 \times 18$

$=77760$

Hence, $48^{3}-30^{3}-18^{3}=77760$.

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Updated on: 10-Oct-2022

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