Evaluate: 25^3-75^3+50^3 - Vidyadip

Question

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

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Answer

Let $a =25, b=-75$ and $c =50$
Then, $a + b + c =25-75+50=0$
$\therefore a ^3+ b ^3+ c ^3=3 abc$
$\Rightarrow(25)^3+(-75)^3+(50)^3$
$=3 \times 25 \times(-75) \times 50=-75 \times 75 \times 50$
$=-5625 \times 50=-281250 \therefore 25^3-75^3+50^3=-281250$

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