Solve p^2-q^2-5p+5q=

$$p ^ { 2 } - q ^ { 2 } - 5 p + 5 q =$$

Factor

$$\left(p-q\right)\left(p+q-5\right)$$

Solution Steps

Consider p^{2}-q^{2}-5p+5q as a polynomial over variable p.

$$p^{2}-5p-q^{2}+5q$$

Find one factor of the form p^{k}+m, where p^{k} divides the monomial with the highest power p^{2} and m divides the constant factor -q^{2}+5q. One such factor is p-q. Factor the polynomial by dividing it by this factor.

$$\left(p-q\right)\left(p+q-5\right)$$

Evaluate

$$\left(p-q\right)\left(p+q-5\right)$$