please solve the sum
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Answer:
54b(27b + 4a²)
Step-by-step explanation:
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - b³ - 3ab(a - b)
(2a + 9b)³ = (2a)³ + (9b)³ + 3×2a×9b(2a + 9b)
= 8a³ + 729b³ + 54ab(2a) + 54ab(9b)
= 8a³ + 729b³ + 108a²b + 468ab²
(2a - 9b)³ = (2a)³ - (9b)³ - 3×2a×9b(2a - 9b)
= 8a³ - 729b³ - 54ab(2a) + 54ab(9b)
= 8a³ - 729b³ - 108a²b + 468ab²
(2a + 9b)³ - (2a - 9b)³ = 8a³ + 729b³ + 108a²b + 468ab² - (8a³ - 729b³ - 108a²b + 468ab²)
= 8a³ + 729b³ + 108a²b + 468ab² - 8a³ + 729b³ + 108a²b - 468ab²
= 729b³ + 729b³ + 108a²b + 108a²b
= 1458b³ + 216a²b
= 54b(27b + 4a²)
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