Evaluate \(22^3 + (-13)^3 + (-9)^3\)
7722
Let \(a = 22\), \(b = -13\) and \(c = -9\).
Their sum \(a + b + c = 22 - 13 - 9 = 0\).
When \(a + b + c = 0\), the identity gives \(a^3 + b^3 + c^3 = 3abc\).
So the value \(= 3 \times 22 \times (-13) \times (-9)\).
Computing: \(3 \times 22 = 66\), and \((-13) \times (-9) = 117\), so \(66 \times 117 = 7722\).
Hence, the value of the expression is 7722.
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