Find the value of $(28)^{3} - (78)^{3} + (50)^{3}$

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Solution

Let $a = 28, b = - 78, c = 50$
Then $a + b + c = 28 - 78 + 50 = 0$
Using, If $(a + b + c) = 0$ ,then $a^{3} + b^{3} + c^{3} = 3 a b c$
$∴ a^{3} + b^{3} + c^{3} = 3 a b c$
So $(28)^{3} + (- 78)^{3} + (50)^{3} = 3 \times 28 \times (- 78) \times 50 = - 327600$

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