Solve c^4-256

$$c ^ { 4 } - 256$$

Factor

$$\left(c-4\right)\left(c+4\right)\left(c^{2}+16\right)$$

Solution Steps

Rewrite c^{4}-256 as \left(c^{2}\right)^{2}-16^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c^{2}-16\right)\left(c^{2}+16\right)$$

Consider c^{2}-16. Rewrite c^{2}-16 as c^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-4\right)\left(c+4\right)$$

Rewrite the complete factored expression. Polynomial c^{2}+16 is not factored since it does not have any rational roots.

$$\left(c-4\right)\left(c+4\right)\left(c^{2}+16\right)$$

Evaluate

$$c^{4}-256$$