Factorize: `a^3-8b^3-64 c^3-24 a b c`

Explanation

We know that
`a^3+b^3+c^3−3abc=(a+b+c)(a^2+b^2+c^2−ab−bc−ca)`
i.e. ,
`a^3+8(-b)^3+64(-c)^3−24abc=(a)^3+(-2b)^3+(-4c)^3−3xxaxx(-2b)xx(-4c)`
`=(a-2b-4c)[(a)^2+(-2b)^2+(-4c)^2−axx(-2b)−(-2b)xx(-4c)−(-4c)xxa]`
`=>``a^3-8b^3-64 c^3-24abc=(a-2b-4c)(a^2+4b^2+16c^2+2ab−8bc+4ca)`