Question

Factorize:
8a³ + 125b³ − 64c³ + 120abc

Answer 1

$$\begin{gathered} 8a^3+125b^3-64c^3+120abc={\left(2a\right)}^3+{\left(5b\right)}^3+{\left(-4c\right)}^3-3\times \left(2a\right)\times \left(5b\right)\times \left(-4c\right) \\ =\left(2a+5b-4c\right)\left[{\left(2a\right)}^2+{\left(5b\right)}^2+{\left(-4c\right)}^2-\left(2a\right)\left(5b\right)-\left(5b\right)\left(-4c\right)-\left(2a\right)\times \left(-4c\right)\right] \\ =\left(2a+5b-4c\right)\left(4a^2+25b^2+16c^2-10ab+20bc+8ac\right) \end{gathered}$$