If a - 2b + 3c = 0; state the value of a3 - 8b3 + 27c3.
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By property,
If x + y + z = 0, then :
x3 + y3 + z3 = 3xyz.
Given,
⇒ a - 2b + 3c = 0
⇒ a + (-2b) + 3c = 0
∴ a3 + (-2b)3 + (3c)3 = 3 × a × (-2b) × 3c
⇒ a3 - 8b3 + 27c3 = -18abc.
Hence, a3 - 8b3 + 27c3 = -18abc.
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