Question

If 2a - 3b = 10 and ab = 16; find the value of 8a³ - 27b³.

Answer 1

2a - 3b = 10
(2a - 3b)³ = (2a)³ - (3b)³ - 2(2a) (3b) (2a - 3b)
⇒ 1000 = 8a³ - 27b³ - 12(16) (10)
⇒ 8a³ - 27b³
= 1000 + 1920
= 2920.