Question

$x^3-8y^3-64z^3-24xyz$

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}{x}^3-8y^3-64z^3-24xyz \\ ={\left(x\right)}^3+{\left(-2y\right)}^3+{\left(-4z\right)}^3-3\times \left(x\right)\times \left(-2y\right)\times \left(-4z\right) \\ =\left[\left(x\right)+\left(-2y\right)+\left(-4z\right)\right]\left[{\left(x\right)}^2+{\left(-2y\right)}^2+{\left(-4z\right)}^2-\left(x\right)\left(-2y\right)-\left(-2y\right)\left(-4z\right)-\left(-4z\right)\left(x\right)\right] \\ =\left(x-2y-4z\right)\left(x^2+4y^2+16z^2+2xy-8yz+4xz\right) \end{gathered}$$