Question

Factorise $a^3+27b^3+8c^3-18abc$.

Answer 1

Put this in the form
$a^3+(3{b)}^3+(2{c)}^3-3a\left(3b\right)\left(2c\right)$
Use the familiar factorisation to get
$a^3+27b^3+8c^3-18abc=(a+3b+2c)[a^2+({3b)}^2+(2{c)}^2-a(3b)-3b(2c)-(2c\left)a\right]$
Now simplify and get
$a^3+27b^3+8c^3-18abc=(a+3b+2c)(a^2+{9b}^2+4c^2-3ab-6bc-2ca)$