If 8(a + b)³ + (a - b)³ = (3a + b) [Aa² + Bb² + Cb²), then what is the value of 2(A + B - C)?

4

8(a + b)³ + (a - b)³ = (3a + b) [Aa² + Bb² + Cb²)

x³ + y³ = (x + y) [x² + y² - xy]

x = 2(a + b)

y = (a - b)

⇒ (2a + 2b + a - b) [(2a + 2b)² + (a - b)² - 2(a + b) (a - b)] = (3a + b) [Aa² + Bb² + Cb²]

⇒ (3a + b) [(2a + 2b)² + (a - b)² - 2(a + b) (a - b)] = (3a + b) [Aa² + Bb² + Cb²]

⇒ (4a² + 4b² + 8ab + a² + b² - 2ab - 2a² + 2b²) = [Aa² + Bab + Cb²]

⇒ 3a² + 7b² + 6ab = Aa² + Bab + Cb²

on comparing, A = 3, B = 6, C = 7

2(A + B - C) = 2(6 + 3 - 7) = 4