Solve w^4-1296

$$w ^ { 4 } - 1296$$

Factor

$$\left(w-6\right)\left(w+6\right)\left(w^{2}+36\right)$$

Solution Steps

Rewrite w^{4}-1296 as \left(w^{2}\right)^{2}-36^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(w^{2}-36\right)\left(w^{2}+36\right)$$

Consider w^{2}-36. Rewrite w^{2}-36 as w^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(w-6\right)\left(w+6\right)$$

Rewrite the complete factored expression. Polynomial w^{2}+36 is not factored since it does not have any rational roots.

$$\left(w-6\right)\left(w+6\right)\left(w^{2}+36\right)$$

Evaluate

$$w^{4}-1296$$