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If a + b + c = 8, then the value of (a – 4)3 + (b – 3)3 + (c – 1)3 – 3 (a – 4) (b – 3) (c – 1) is
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- 2
- 4
- 1
- 0
Correct Option: D
We have p3 + q3 + r3 – 3pqr = (p + q + r) (p2 + q2 + r2 –pq – qr - rp)
Here p = a – 4, q = b – 3, r = c –1
So, given expression is (p + q + r) (p2 + q2 + r2 – pq – qr – rp)
= (a – 4 + b – 3 + c – 1) (p2 + q2 + r2 – pq – qr – rp)
= (a + b + c – 8) (p2 + q2 + r2 – pq – qr – rp)
= (8 – 8) (p2 + q2 + r2 – pq – qr – rp)
∴ (a – 4)3 + (b – 3)3 + (c – 1)3 – 3 (a – 4) (b – 3) (c – 1) = 0
