If p = 2 – a, then a3 + 6 ap + p3

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If p = 2 – a, then a³ + 6 ap + p³ – 8 = ?

1. 0
2. 8
3. 6
4. 5

Correct Option: A

p = 2 – a ⇒ a + p – 2 = 0
∴ a³ + 6ap + p³ – 8
= a³ + p³ + (–2)³ – 3ap (–2)
= (a + p – 2) {a² + p² + (–2)² – ap – p (–2) – a (–2)}
= (a + p – 2) (a² + p² + 4 – ap + 2p + 2a) = 0