Question

factorise a cube -8b cube -64c cube -24 abc

Answer 1

$a^{3}-8b^{3}-64c^{3}-24abc=a^{3}+(-2b)^{3}+(-4c)^{3}-3(a)(-2b)(-4c)$
We have a formula that:
x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
Put x=a, y=-2b and z=-4c
So,
$a^{3}-8b^{3}-64c^{3}-24abc$=(a-2b-4c)(a^2+4b^2+16c^2-4ab-8ac                                                                       +16bc)