Solve a-b-a^2+b^2

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

Factor

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

Solution Steps

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

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

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

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

Evaluate

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