Question

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

Answer 1

(x – y − z) (x² + y² + z² + xy – yz + xz)
$$\begin{gathered} =(x+\left(-y\right)+\left(-z\right))(x^2+y^2+z^2+xy–yz+xz) \\ \mathrm{We}\mathrm{know} \\ \left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)=a^3+b^3+c^3-3abc \\ \mathrm{Here},a=x,b=-y,c=-z \\ (x+\left(-y\right)+\left(-z\right))(x^2+y^2+z^2+xy–yz+xz)=x^3-y^3-z^3-3xyz \end{gathered}$$