Solve m^2+2mn-8n^2

$${ m }^{ 2 } +2mn-8 { n }^{ 2 }$$

Factor

$$\left(m-2n\right)\left(m+4n\right)$$

Solution Steps

Consider m^{2}+2mn-8n^{2} as a polynomial over variable m.

$$m^{2}+2nm-8n^{2}$$

Find one factor of the form m^{k}+p, where m^{k} divides the monomial with the highest power m^{2} and p divides the constant factor -8n^{2}. One such factor is m+4n. Factor the polynomial by dividing it by this factor.

$$\left(m+4n\right)\left(m-2n\right)$$

Evaluate

$$\left(m-2n\right)\left(m+4n\right)$$