Evaluate:$ 25^{3}-75^{3}+50^{3} $

Given: 

\( 25^{3}-75^{3}+50^{3} \)

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 $a=25, b=-75$ and $c=50$

$a+b+c=25-75+50=0$

This implies,

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

$25^{3}-75^{3}+50^{3}=3 \times 25 \times(-75) \times 50$

$=-3 \times 25 \times 75 \times 50$

$=-281250$

Hence, $25^{3}-75^{3}+50^{3}=-281250$.

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Updated on: 10-Oct-2022

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