Solve a^4n-b^4n=

$$a ^ { 4 n } - b ^ { 4 n } =$$

Factor

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

Solution Steps

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

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

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

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

Evaluate

$$a^{4n}-b^{4n}$$