Solve p+q+p^2-q^2

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

Factor

$$\left(p+q\right)\left(p-q+1\right)$$

Solution Steps

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

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

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}+q. One such factor is p+q. Factor the polynomial by dividing it by this factor.

$$\left(p+q\right)\left(p-q+1\right)$$

Evaluate

$$\left(p+q\right)\left(p-q+1\right)$$