Solve p^2q^2-mb-p^2b^2-mq

$$p ^ { 2 } q ^ { 2 } - m b - p ^ { 2 } b ^ { 2 } - m q$$

Factor

$$\left(q+b\right)\left(qp^{2}-bp^{2}-m\right)$$

Solution Steps

Consider p^{2}q^{2}-mb-p^{2}b^{2}-mq as a polynomial over variable q.

$$p^{2}q^{2}-mq-mb-p^{2}b^{2}$$

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

$$\left(q+b\right)\left(-m-bp^{2}+qp^{2}\right)$$

Evaluate

$$\left(q+b\right)\left(qp^{2}-bp^{2}-m\right)$$