Solve c+d-c^2+d^2

$$c + d - c ^ { 2 } + d ^ { 2 }$$

Factor

$$\left(-c-d\right)\left(c-d-1\right)$$

Solution Steps

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

$$-c^{2}+c+d+d^{2}$$

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

$$\left(-c-d\right)\left(c-d-1\right)$$

Evaluate

$$d+d^{2}+c-c^{2}$$