Question

$-$27x³ + y³ $-$ z³ $-$ 9xyz

Answer 1

$$\begin{gathered} -27x^3+y^3-z^3-9xyz \\ ={\left(-3x\right)}^3+{\left(y\right)}^3+{\left(-z\right)}^3-3\times \left(-3x\right)\left(y\right)\left(-z\right) \\ =\left[\left(-3x\right)+\left(y\right)+\left(-z\right)\right]\left[{\left(-3x\right)}^2+{\left(y\right)}^2+{\left(-z\right)}^2-\left(-3x\right)\times \left(y\right)-\left(y\right)\times \left(-z\right)-\left(-z\right)\times \left(-3x\right)\right] \\ =\left(-3x+y-z\right)\left(9x^2+y^2+z^2+3xy+yz-3zx\right) \end{gathered}$$