Solve v^4-10000

$$v ^ { 4 } - 10000$$

Factor

$$\left(v-10\right)\left(v+10\right)\left(v^{2}+100\right)$$

Solution Steps

Rewrite v^{4}-10000 as \left(v^{2}\right)^{2}-100^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v^{2}-100\right)\left(v^{2}+100\right)$$

Consider v^{2}-100. Rewrite v^{2}-100 as v^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-10\right)\left(v+10\right)$$

Rewrite the complete factored expression. Polynomial v^{2}+100 is not factored since it does not have any rational roots.

$$\left(v-10\right)\left(v+10\right)\left(v^{2}+100\right)$$

Evaluate

$$v^{4}-10000$$