Solve x^4-pi^4

$${ x }^{ 4 } - { \pi }^{ 4 }$$

Factor

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

Solution Steps

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

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

Consider x^{2}-\pi ^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right). Polynomial x^{2}+\pi ^{2} is not factored since it does not have any rational roots.

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

Evaluate

$$x^{4}-\pi ^{4}$$