Solve 1000+8v^6

$$1000 + 8 v ^ { 6 }$$

Factor

$$8\left(v^{2}+5\right)\left(v^{4}-5v^{2}+25\right)$$

Solution Steps

Factor out 8.

$$8\left(125+v^{6}\right)$$

Consider 125+v^{6}. Rewrite 125+v^{6} as \left(v^{2}\right)^{3}+5^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(v^{2}+5\right)\left(v^{4}-5v^{2}+25\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: v^{2}+5,v^{4}-5v^{2}+25.

$$8\left(v^{2}+5\right)\left(v^{4}-5v^{2}+25\right)$$

Evaluate

$$8\left(v^{6}+125\right)$$