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Algebraic Identities

Write the val...

Question

Write the value of $48^{3} - 30^{3} - 18^{3} .$

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Solution

$48^{3} - 30^{3} - 18^{3} .$
Let $a = 48, b = - 30, c = - 18 ∵ a + b + c = 48 - 30 - 18 = 0 ∴ a^{3} + b^{3} + c^{3} = 3 a b c \Rightarrow 48^{3} - 30^{3} - 18^{3} = 3 \times 48 \times (- 30) (- 18) = 77760$

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