# How do you factor 125+8z^3?

Dec 24, 2015

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

#### Explanation:

This is a sum of cube because

$125 = {5}^{3}$

$8 {z}^{3} = {\left(2 z\right)}^{3}$

Remember the formula for sum of cube is

${x}^{3} + {y}^{3} = \left(x + y\right) \left({x}^{2} - x y + {y}^{2}\right)$

We can rewrite $125 + 8 {z}^{3} = {5}^{3} + {\left(2 z\right)}^{3}$

This factor to

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

or we can rewrite the factor as

$\left(2 z + 5\right) \left(4 {z}^{2} - 10 z + 25\right)$ so it can be in alphabetical order (standard form for polynomial)