Solve x^4-256?

$$x ^ { 4 } - 256 ?$$

Factor

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

Solution Steps

Rewrite x^{4}-256 as \left(x^{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).

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

Consider x^{2}-16. Rewrite x^{2}-16 as x^{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).

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

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

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

Evaluate

$$x^{4}-256$$