Write the value of $25^{3} - 75^{3} + 50^{3} .$

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Solution

$25^{3} - 75^{3} + 50^{3} L e t a = 25, b = - 75 a n d c = 50 ∵ a + b + c = 25 - 75 + 50 = 0 ∴ a^{3} + b^{3} + c^{3} = 3 a b c \Rightarrow 25^{3} + (- 75)^{3} + 50^{3} = 3 \times 25 \times (- 75) \times 50 = - 281250$

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