# How do you factor 8x³ + 125y³?

May 12, 2018

$\left(2 x + 5 y\right) {\left(2 x - 5 y\right)}^{2}$

#### Explanation:

$8 {x}^{3} + 125 {y}^{3}$ is ${\left(2 x\right)}^{3} + {\left(5 y\right)}^{3}$

the sum of two cubes formula
${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$

so

${\left(2 x\right)}^{3} + {\left(5 y\right)}^{3}$

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

now you can factor the second parentheses pair
$\left(2 x + 5 y\right) \textcolor{red}{\left(4 {x}^{2} - 10 x y + 25 {y}^{2}\right)}$

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

$\left(2 x + 5 y\right) {\left(2 x - 5 y\right)}^{2}$