Question

Find the product (a − b − c) (a² + b² + c² + ab + ac − bc).

Answer 1

$$\begin{gathered} \left(a-b-c\right)\left(a^2+b^2+c^2+ab+ac-bc\right) \\ =\left[a+\left(-b\right)+\left(-c\right)\right]\left[{\left(a\right)}^2+\left(-b^2\right)+{\left(-c\right)}^2-\left(a\right)\left(-b\right)-\left(a\right)\left(-c\right)-\left(-b\right)\left(-c\right)\right] \\ ={\left(a\right)}^3+{\left(-b\right)}^3+{\left(-c\right)}^3-3\left(a\right)\left(-b\right)\left(-c\right) \\ =a^3-b^3-c^3-3abc \end{gathered}$$