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Without actua...

Question

Without actual division find $27^{3} - 25^{3} - 2^{3}$

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Solution

$(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b) (a + b)^{3} - a^{3} - b^{3} = 3 a b (a + b) 27^{3} - 25^{3} - 2^{3} = 3 (25) (2) (27) 4050$

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