Question

Find the product:
(x − 2y − z) (x² + 4y² + z² + 2xy + zx − 2yz)

Answer 1

$$\begin{gathered} \left(x-2y-z\right)\left(x^2+4y^2+z^2+2xy+zx-2yz\right) \\ =\left(x-2y-z\right)\left(x^2+4y^2+z^2+2xy-2yz+zx\right) \\ =\left[x+\left(-2y\right)+\left(-z\right)\right]\left[x^2+4y^2+z^2-x\times \left(-2y\right)-\left(-2y\right)\left(-z\right)-\left(-z\right)\times x\right] \\ ={\left(x\right)}^3+{\left(-2y\right)}^3+{\left(-z\right)}^3-3\times x\left(-2y\right)\times \left(-z\right) \\ =x^3-8y^3-z^3-6xyz \end{gathered}$$