Solve v^4x^4-x^4

$$v ^ { 4 } x ^ { 4 } - x ^ { 4 }$$

Factor

$$\left(v-1\right)\left(v+1\right)\left(v^{2}+1\right)x^{4}$$

Solution Steps

Factor out x^{4}.

$$x^{4}\left(v^{4}-1\right)$$

Consider v^{4}-1. Rewrite v^{4}-1 as \left(v^{2}\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v^{2}-1\right)\left(v^{2}+1\right)$$

Consider v^{2}-1. Rewrite v^{2}-1 as v^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-1\right)\left(v+1\right)$$

Rewrite the complete factored expression. Polynomial v^{2}+1 is not factored since it does not have any rational roots.

$$x^{4}\left(v-1\right)\left(v+1\right)\left(v^{2}+1\right)$$

Evaluate

$$x^{4}\left(v^{4}-1\right)$$