If x + y + z = 9 then the value of (x – 4)3 + (y

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If x + y + z = 9 then the value of (x – 4)³ + (y – 2)³ + (z – 3)³ – 3 (x – 4) (y – 2) (z – 3) is

1. 6
2. 9
3. 0
4. 1

Correct Option: C

If a + b + c = 0, then a³ + b³ + c³ – 3abc = 0
Here, x – 4 + y – 2 + z – 3
= x + y + z – 9 = 9 – 9 = 0
∴ (x – 4)³ + (y – 2)³ + (z – 3)³ – 3
(x – 4) (y – 2) (z – 3) = 0