Question

Expand the following:

(5a + 4b)³

Answer 1

Using the identity

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, let a = 5a, b = 4b

(5a + 4b)³ = (5a)³ + 3(5a)² × 4b + 3 × 5a(4b)² + (4b)³

= 125a³ + 3(25a² × 4b) + 3(5a × 16b²) + 64b³

= 125a³ + 3(100a²b) + 3(80ab²) + 64b³

∴ (5a + 4b)³ = 125a³ + 300a²b + 240ab² + 64b³