Question

Find the product:

(x² − xy + y²)(x + y)

Answer 1

By column method:

$$\begin{gathered} {\mathrm{x}}^2-\mathrm{xy}+{\mathrm{y}}^2 \\ \underline{\times (\mathrm{x}+\mathrm{y})} \\ {\mathrm{x}}^3-{\mathrm{x}}^2\mathrm{y}+{\mathrm{xy}}^2 \\ \underline{{\mathrm{x}}^2\mathrm{y}-{\mathrm{xy}}^2+{\mathrm{y}}^3} \\ \mathrm{Add}:{\mathrm{x}}^3+{\mathrm{y}}^3 \\ \therefore ({\mathrm{x}}^2-\mathrm{xy}+{\mathrm{y}}^2)(\mathrm{x}+\mathrm{y})={\mathrm{x}}^3+{\mathrm{y}}^3 \end{gathered}$$