Solve m^2n^4-m^6

$$m ^ { 2 } n ^ { 4 } - m ^ { 6 }$$

Factor

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

Solution Steps

Factor out m^{2}.

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

Consider n^{4}-m^{4}. Rewrite n^{4}-m^{4} as \left(n^{2}\right)^{2}-\left(m^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Reorder the terms.

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

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

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

Reorder the terms.

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

Rewrite the complete factored expression.

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

Evaluate

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