Question

Factorize:
27a³ − b³ + 8c³ + 18abc

Answer 1

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