Question
Evaluate:
$25^3-75^3+50^3$
$25^3-75^3+50^3$
✓
Answer
Let $\mathrm{a}=25, \mathrm{~b}=-75$ and $\mathrm{c}=50$
Then,
$a+b+c=25-75+50$
$=0$
$\therefore a^3+b^3+c^3=3 a b c$
$\Rightarrow(25)^3+(-75)^3+(50)^3=3 \times 25 \times(-75) \times 50$
$=-75 \times 75 \times 50$
$=-5625 \times 50$
$=-281250$
$\therefore 25^3-75^3+50^3=-281250$
Then,
$a+b+c=25-75+50$
$=0$
$\therefore a^3+b^3+c^3=3 a b c$
$\Rightarrow(25)^3+(-75)^3+(50)^3=3 \times 25 \times(-75) \times 50$
$=-75 \times 75 \times 50$
$=-5625 \times 50$
$=-281250$
$\therefore 25^3-75^3+50^3=-281250$
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