Question

Expand the following:

(5ab + 2)³

Answer 1

Using the identity

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, let a = 5ab, b = 2

(5ab + 2)³ = (5ab)³ + 3(5ab)²(2) + 3(5ab) (2²) + (2)³

= 125a³b³ + 3(25a²b²)(2) + 3(5ab)(4) + 8

= 125a³b³ + 6(25a²b²) + 12(5ab) + 8

∴ (5ab + 2)³ = 125a³b³ + 150a²b² + 60ab + 8