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Question
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
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Solution
Given, (0.2)3 – (0.3)3 + (0.1)3 or (0.2)3 + (–0.3)3 + (0.1)3
Here, we see that,
0.2 – 0.3 + 0.1 = 0.3 – 0.3 = 0
∴ (0.2)3 + (–0.3)3 + (0.1)3 = 3 × (0.2) × (–0.3) × (0.1) ...[Using identity, if a + b + c = 0, then a3 + b3 + c3 = 3abc]
= –0.6 × 0.03
= –0.018
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