Solve -64m^4-8m^2n-1/4n^2

$$- 64 m ^ { 4 } - 8 m ^ { 2 } n - \frac { 1 } { 4 } n ^ { 2 }$$

Factor

$$-\frac{\left(16m^{2}+n\right)^{2}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{-256m^{4}-32m^{2}n-n^{2}}{4}$$

Consider -256m^{4}-32m^{2}n-n^{2}. Consider -256m^{4}-32m^{2}n-n^{2} as a polynomial over variable m.

$$-256m^{4}-32nm^{2}-n^{2}$$

Find one factor of the form km^{p}+q, where km^{p} divides the monomial with the highest power -256m^{4} and q divides the constant factor -n^{2}. One such factor is 16m^{2}+n. Factor the polynomial by dividing it by this factor.

$$\left(16m^{2}+n\right)\left(-16m^{2}-n\right)$$

Rewrite the complete factored expression.

$$\frac{\left(16m^{2}+n\right)\left(-16m^{2}-n\right)}{4}$$

Evaluate

$$-\frac{\left(16m^{2}+n\right)^{2}}{4}$$