Solve (2m^3n)^2-4(m^2n)^2

$$( 2 m ^ { 3 n } ) ^ { 2 } - 4 ( m ^ { 2 n } ) ^ { 2 }$$

Factor

$$4\left(m^{n}-1\right)\left(m^{n}+1\right)\left(m^{n}\right)^{4}$$

Solution Steps

Factor out 4.

$$4\left(\left(m^{3n}\right)^{2}-\left(m^{2n}\right)^{2}\right)$$

Consider \left(m^{n}\right)^{6}-\left(m^{n}\right)^{4}. Factor out \left(m^{n}\right)^{4}.

$$\left(m^{n}\right)^{4}\left(\left(m^{n}\right)^{2}-1\right)$$

Consider \left(m^{n}\right)^{2}-1. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m^{n}-1\right)\left(m^{n}+1\right)$$

Rewrite the complete factored expression.

$$4\left(m^{n}\right)^{4}\left(m^{n}-1\right)\left(m^{n}+1\right)$$

Evaluate

$$4\left(m^{6n}-m^{4n}\right)$$