Question

a³ $-$ b³ + 8c³ + 6abc

Answer 1

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