Solve m^2-mv-56v^2

$$m ^ { 2 } - m v - 56 v ^ { 2 }$$

Factor

$$\left(m-8v\right)\left(m+7v\right)$$

Solution Steps

Consider m^{2}-mv-56v^{2} as a polynomial over variable m.

$$m^{2}-vm-56v^{2}$$

Find one factor of the form m^{k}+n, where m^{k} divides the monomial with the highest power m^{2} and n divides the constant factor -56v^{2}. One such factor is m-8v. Factor the polynomial by dividing it by this factor.

$$\left(m-8v\right)\left(m+7v\right)$$

Evaluate

$$\left(m-8v\right)\left(m+7v\right)$$