Solve n^2-2nm+m^2+5n-5m

$$n ^ { 2 } - 2 n m + m ^ { 2 } + 5 n - 5 m$$

Factor

$$\left(n-m\right)\left(5+n-m\right)$$

Solution Steps

Consider n^{2}-2nm+m^{2}+5n-5m as a polynomial over variable n.

$$n^{2}+\left(-2m+5\right)n+m^{2}-5m$$

Find one factor of the form n^{k}+p, where n^{k} divides the monomial with the highest power n^{2} and p divides the constant factor m^{2}-5m. One such factor is -m+n. Factor the polynomial by dividing it by this factor.

$$\left(-m+n\right)\left(-m+n+5\right)$$

Evaluate

$$\left(n-m\right)\left(5+n-m\right)$$