Solve 2a^{2}b^2-2ab^2-a^2b-a^2-2ab+a+b

$$2 a ^ { 2 } b ^ { 2 } - 2 a b ^ { 2 } - a ^ { 2 } b - a ^ { 2 } - 2 a b + a + b$$

Factor

$$\left(2ab+a-1\right)\left(ab-a-b\right)$$

Solution Steps

Consider 2a^{2}b^{2}-2ab^{2}-a^{2}b-a^{2}-2ab+a+b as a polynomial over variable b.

$$\left(2a^{2}-2a\right)b^{2}+\left(-a^{2}-2a+1\right)b-a^{2}+a$$

Find one factor of the form kb^{m}+n, where kb^{m} divides the monomial with the highest power \left(2a^{2}-2a\right)b^{2} and n divides the constant factor -a^{2}+a. One such factor is 2ab+a-1. Factor the polynomial by dividing it by this factor.

$$\left(2ab+a-1\right)\left(ab-a-b\right)$$

Evaluate

$$\left(2ab+a-1\right)\left(ab-a-b\right)$$