Solve (4)(a^{2}b)^2n-(a^2nb^n)^2

$$( 4 ) ( a ^ { 2 } b ) ^ { 2 n } - ( a ^ { 2 n } b ^ { n } ) ^ { 2 }$$

Factor

$$4\left(ba^{2}\right)^{2n}-a^{4n}b^{2n}$$

Solution Steps

The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Evaluate

$$4\left(ba^{2}\right)^{2n}-a^{4n}b^{2n}$$