Solve r^4-4096

$$r ^ { 4 } - 4096$$

Factor

$$\left(r-8\right)\left(r+8\right)\left(r^{2}+64\right)$$

Solution Steps

Rewrite r^{4}-4096 as \left(r^{2}\right)^{2}-64^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r^{2}-64\right)\left(r^{2}+64\right)$$

Consider r^{2}-64. Rewrite r^{2}-64 as r^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-8\right)\left(r+8\right)$$

Rewrite the complete factored expression. Polynomial r^{2}+64 is not factored since it does not have any rational roots.

$$\left(r-8\right)\left(r+8\right)\left(r^{2}+64\right)$$

Evaluate

$$r^{4}-4096$$