Solve 14mn^2-7n^4-7m^2

$$14 m n ^ { 2 } - 7 n ^ { 4 } - 7 m ^ { 2 }$$

Factor

$$-7\left(n^{2}-m\right)^{2}$$

Solution Steps

Factor out 7.

$$7\left(2mn^{2}-n^{4}-m^{2}\right)$$

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

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

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 -n^{4}. One such factor is m-n^{2}. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression.

$$7\left(m-n^{2}\right)\left(-m+n^{2}\right)$$

Evaluate

$$-7\left(n^{2}-m\right)^{2}$$