Question

Factorize:
216 + 27b³ + 8c³ − 108abc

Answer 1

$$\begin{gathered} 216+27b^3+8c^3-108abc={\left(6\right)}^3+{\left(3b\right)}^3+{\left(2c\right)}^3-3\times 6\times 3b\times 2c \\ =\left(6+3b+2c\right)\left[6^2+{\left(3b\right)}^2+{\left(2c\right)}^2-6\times 3b-3b\times 2c-2c\times 6\right] \\ =\left(6+3b+2c\right)\left(36+9b^2+4c^2-18b-6bc-12c\right) \end{gathered}$$