Question

factorise by grouping the terms :p2q _pr2_pq+r2

Answer 1

$$\begin{gathered} {\mathrm{p}}^2\mathrm{q}-{\mathrm{pr}}^2-\mathrm{pq}+{\mathrm{r}}^2={\mathrm{p}}^2\mathrm{q}-\mathrm{pq}-{\mathrm{pr}}^2+{\mathrm{r}}^2 \\ =\mathrm{pq}\left(\mathrm{p}-1\right)-{\mathrm{r}}^2\left(\mathrm{p}-1\right) \\ =\left(\mathrm{p}-1\right)\left(\mathrm{pq}-{\mathrm{r}}^2\right) \\ \mathrm{Hence},{\mathbf{p}}^{\mathbf{2}}\mathbf{q}\mathbf{-}{\mathbf{pr}}^{\mathbf{2}}\mathbf{-}\mathbf{pq}\mathbf{+}{\mathbf{r}}^{\mathbf{2}}\mathbf{=}\left(\mathbf{p}\mathbf{-}\mathbf{1}\right)\left(\mathbf{pq}\mathbf{-}{\mathbf{r}}^{\mathbf{2}}\right) \end{gathered}$$