Question

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

Answer 1

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