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Without actually calculating the cubes, find the value of the following:- (–12)^{3} + (7)^{3} + (5)^{3}

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#### Solution

(–12)^{3} + (7)^{3} + (5)^{3}

Let *x* = −12, *y* = 7, and *z* = 5

It can be observed that,

*x* + *y* + *z* = − 12 + 7 + 5 = 0

It is known that if *x* + *y* + *z* = 0, then

x^{3} + y^{3} + z^{3} = 3xyz

∴ (–12)^{3} + (7)^{3} + (5)^{3} = 3(-12)(7)(5) = -1260

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