Solve v^4-1296

$$v ^ { 4 } - 1296$$

Factor

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

Solution Steps

Rewrite v^{4}-1296 as \left(v^{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).

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

Consider v^{2}-36. Rewrite v^{2}-36 as v^{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).

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

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

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

Evaluate

$$v^{4}-1296$$