Solve 6n^4-6

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

Factor

$$6\left(n-1\right)\left(n+1\right)\left(n^{2}+1\right)$$

Solution Steps

Factor out 6.

$$6\left(n^{4}-1\right)$$

Consider n^{4}-1. Rewrite n^{4}-1 as \left(n^{2}\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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

$$\left(n-1\right)\left(n+1\right)$$

Rewrite the complete factored expression. Polynomial n^{2}+1 is not factored since it does not have any rational roots.

$$6\left(n-1\right)\left(n+1\right)\left(n^{2}+1\right)$$

Evaluate

$$6\left(n^{4}-1\right)$$