Question

Expand the following:

(3a + b)³

Answer 1

Given: Expand (3a + b)³.

Step-wise calculation:

We use the binomial expansion formula for the cube of a sum:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, a = 3a and b = b.

Substitute:

(3a + b)³ = (3a)³ + 3(3a)²(b) + 3(3a)(b)² + b³

Calculate each term:

(3a)³ = 27a³

3(3a)²b = 3 × 9a² × b = 27a²b

3(3a)(b)² = 9ab²

b³ = b³

Sum all:

27a³ + 27a²b + 9ab² + b³