Without actually calculating cubes find the following (0.2)³-(0.3)³+(0.1)³

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Solution

using identity:
x³ + y³ + z³- 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx)

if x + y + z = 0,

then, x³ + y³ + z³- 3xyz = 0

or x³ + y³ + z³= 3xyz

(0.2)³ - (0.3)³ + (0.1)³can be written as
(0.2)³+ (-0.3)³ + (0.1)³ //since (-x)³ = -x³ //

here, (0.2) + (-0.3) + (0.1) = 0.3 - 0.3 = 0

so, (0.2)³ - (0.3)³ + (0.1)³ =

3*(0.2)(-0.3)(0.1) = - 0.018

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