Evaluate \(22^3 + (-15)^3 + (-7)^3\)
6930
Let \(a = 22\), \(b = -15\), \(c = -7\). Then \(a + b + c = 22 - 15 - 7 = 0\).
The identity states that when \(a + b + c = 0\), then \(a^3 + b^3 + c^3 = 3abc\).
So \(a^3 + b^3 + c^3 = 3 \times 22 \times (-15) \times (-7)\).
\(= 3 \times 22 \times 105 = 6930\).
Hence, the value of the expression is 6930.
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