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

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

Factor

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

Solution Steps

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

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

Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{2} and m 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

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