If a + 2b + 3c = 0, then what is the value of ($$a^3 + 8b^3 + 27c^3$$​)?

Correct option is A

Given:

The equation is a + 2b + 3c = 0.

Formula Used:

​$$x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)$$​​

Solution:

Put x = a, y = 2b, z = 3c in above formula,

​$$=a^3 + 8b^3 + 27c^3 - 3(a)(2b)(3c)\\ \ \\ = (a + 2b + 3c)(a^2 + (2b)^2 + (3c)^2 - a(2b) - 2b(3c) - 3c(a))$$​​

Since a + 2b + 3c = 0, the right-hand side becomes 0:

​$$a^3 + 8b^3 + 27c^3 - 18abc = 0$$​​

​$$a^3 + 8b^3 + 27c^3 = 18abc$$​