Solve w^4-4096

$$w ^ { 4 } - 4096$$

Factor

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

Solution Steps

Rewrite w^{4}-4096 as \left(w^{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).

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

Consider w^{2}-64. Rewrite w^{2}-64 as w^{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).

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

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

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

Evaluate

$$w^{4}-4096$$