Question

Expand the following:

(2a + 3b)³

Answer 1

Using the identity:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, let a = 2a, b = 3b

(2a + 3b)³ = (2a)³ + 3(2a)² (3b) + 3(2a) (3b)² + (3b)³

= 8a³ + (2a)²(9b) + (6a)(3b)² + 27b³

= 8a³ + 4a² × 9b + 6a × 9b² + 27b³

∴ (2a + 3b)³ = 8a³ + 36a²b + 54ab² + 27b³