Solve n^4-6561

$$n ^ { 4 } - 6561$$

Factor

$$\left(n-9\right)\left(n+9\right)\left(n^{2}+81\right)$$

Solution Steps

Rewrite n^{4}-6561 as \left(n^{2}\right)^{2}-81^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n^{2}-81\right)\left(n^{2}+81\right)$$

Consider n^{2}-81. Rewrite n^{2}-81 as n^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-9\right)\left(n+9\right)$$

Rewrite the complete factored expression. Polynomial n^{2}+81 is not factored since it does not have any rational roots.

$$\left(n-9\right)\left(n+9\right)\left(n^{2}+81\right)$$

Evaluate

$$n^{4}-6561$$