Solve 125y^6+2^3

$$125 y ^ { 6 } + 2 ^ { 3 }$$

Factor

$$\left(5y^{2}+2\right)\left(25y^{4}-10y^{2}+4\right)$$

Solution Steps

Multiply and combine like terms.

$$125y^{6}+8$$

Rewrite 125y^{6}+8 as \left(5y^{2}\right)^{3}+2^{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). The following polynomials are not factored since they do not have any rational roots: 5y^{2}+2,25y^{4}-10y^{2}+4.

$$\left(5y^{2}+2\right)\left(25y^{4}-10y^{2}+4\right)$$

Evaluate

$$125y^{6}+8$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$125y^{6}+8$$