If x + 3y + 2z = 0, the value of x³ + 27y³ + 8z³ is :

1. 9xyz

2. 6xyz

3. 18xyz

4. xyz

By property,

If a + b + c = 0, then

a³ + b³ + c³ = 3abc ….(1)

Comparing equation x + 3y + 2z = 0, with a + b + c = 0, we get :

a = x, b = 3y and c = 2z.

Substituting values in equation (1), we get :

x³ + (3y)³ + (2z)³ = 3 × x × 3y × 2z = 18xyz.

Hence, Option 3 is the correct option.