Solve mn-m^2+6n^2

$$m n - m ^ { 2 } + 6 n ^ { 2 }$$

Factor

$$-\left(m-3n\right)\left(m+2n\right)$$

Solution Steps

Consider mn-m^{2}+6n^{2} as a polynomial over variable m.

$$-m^{2}+nm+6n^{2}$$

Find one factor of the form km^{p}+q, where km^{p} divides the monomial with the highest power -m^{2} and q divides the constant factor 6n^{2}. One such factor is m-3n. Factor the polynomial by dividing it by this factor.

$$\left(m-3n\right)\left(-m-2n\right)$$

Evaluate

$$-\left(m-3n\right)\left(m+2n\right)$$