Solve m^4n^2-n^4m^2

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

Factor

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

Solution Steps

Factor out m^{2}n^{2}.

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

Consider m^{2}-n^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Rewrite the complete factored expression.

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

Evaluate

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