If p – 2q = 4, then the value of p³

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If p – 2q = 4, then the value of p³ – 8q³ – 24pq – 64 is :

1. 2
2. 0
3. 3
4. –1

Correct Option: B

Using Rule 9,
p – 2q = 4
On cubing both sides,
(p – 2q)³ = 64
⇒ p³ - 8q³ + 3p.4q² - 3p².2q = 64
⇒ p³ - 8q³ + 12pq² - 6p²q = 64
⇒ p³ - 8q³ + 6pq(p – 2q) = 64
⇒ p³ - 8q³ + 6pq × 4 = 64
⇒ p³ - 8q³ – 24pq – 64 = 0