Solve p^2q-pr^2-pq+r^2

$$p ^ { 2 } q - p r ^ { 2 } - p q + r ^ { 2 }$$

Factor

$$\left(p-1\right)\left(pq-r^{2}\right)$$

Solution Steps

Do the grouping p^{2}q-pr^{2}-pq+r^{2}=\left(p^{2}q-pr^{2}\right)+\left(-pq+r^{2}\right), and factor out p in the first and -1 in the second group.

$$p\left(pq-r^{2}\right)-\left(pq-r^{2}\right)$$

Factor out common term pq-r^{2} by using distributive property.

$$\left(pq-r^{2}\right)\left(p-1\right)$$

Evaluate

$$\left(p-1\right)\left(pq-r^{2}\right)$$