Evaluate: (0.2)3 – (0.3)3 + (0.1)3 without actually calculating the cubes.
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The value of (0.2)³ - (0.3)³ + (0.1)³ is -0.018
Step-by-step explanation:
We know that
a³ + b³ + c³ = (a + b + c)³ - 3(a + b)(b + c)(c + a)
(0.2)³- (0.3)³ + (0.1)³
= (0.2)³ + (-0.3)³ + (0.1)³
= (0.2 - 0.3 + 0.1)³ - 3(0.2 - 0.3)(-0.3 + 0.1)(0.1 + 0.2)
= (0)³- 3(-0.1)(-0.2)(0.3)
= 0 - 0.018
= -0.018
Hence, the value of (0.2)³ - (0.3)³ + (0.1)³ is -0.018
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