Solve 4m^2-16n^2-4n+2m/

$$\frac{ 4 { m }^{ 2 } -16 { n }^{ 2 } -4n+2m }{ }$$

Factor

$$2\left(m-2n\right)\left(2m+4n+1\right)$$

Solution Steps

Factor out 2.

$$2\left(2m^{2}-8n^{2}-2n+m\right)$$

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

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

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

$$\left(m-2n\right)\left(2m+4n+1\right)$$

Rewrite the complete factored expression.

$$2\left(m-2n\right)\left(2m+4n+1\right)$$

Evaluate

$$2\left(m-2n\right)\left(2m+4n+1\right)$$

Solution Steps

Anything divided by one gives itself.

$$4m^{2}-16n^{2}-4n+2m$$