# How do you factor 125a^3-c^3?

Jan 11, 2016

$125 {a}^{3} - {c}^{3} = \left(5 a - c\right) \cdot \left(25 {a}^{2} + 5 a c + {c}^{2}\right)$

#### Explanation:

$125 {a}^{3} - {c}^{3} = {5}^{3} {a}^{3} - {c}^{3} = {\left(5 a\right)}^{3} - {c}^{3}$

Using the difference of two cubes rule:

$\left({b}^{3} - {d}^{3}\right) = \left(b - d\right) \left({b}^{2} + b d + {d}^{2}\right)$

with:

$b = 5 a$
$d = c$

$125 {a}^{3} - {c}^{3} = \left(5 a - c\right) \left({5}^{2} {a}^{2} + 5 a c + {c}^{2}\right) =$
$= \left(5 a - c\right) \cdot \left(25 {a}^{2} + 5 a c + {c}^{2}\right)$