Factorize the following expression : \(x^3 + 6x^2 + 12x + 16\)

\[ x^3 + 6x^2 + 12x + 16 \] \[ = x^3 + 2^3 + 6x^2 + 12x \] \[ = (x + 2)(x^2 – 2x + 4) + 6x(x + 2) \] \[ = (x + 2)(x^2 + 4x + 4) \] \[ = (x + 2)(x + 2)^2 \] \[ = (x + 2)^3 \]