a - b + c = 0
a = b - c
a³ - b³ + c³ = (b - c)³ - b³ + c³ = b³ - 3b²c + 3bc² - c³ - b³ + c³ =
= - 3b²c + 3bc² = 3bc(c - b) = 3bc * (- a) = - 3abc
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Verified answer
a - b + c = 0
a = b - c
a³ - b³ + c³ = (b - c)³ - b³ + c³ = b³ - 3b²c + 3bc² - c³ - b³ + c³ =
= - 3b²c + 3bc² = 3bc(c - b) = 3bc * (- a) = - 3abc