# How do you factor 2r^3 + 250?

Mar 28, 2018

$2 {r}^{3} + 250 = 2 \left(r + 5\right) \left({r}^{2} - 5 r + 25\right)$

#### Explanation:

$2 {r}^{3} \mathmr{and} 250$

$\text{Q.}$ What is the common term?
$\text{A.} 2$

Factor it out:
$2 {r}^{3} + 250 = 2 \left({r}^{3} + 125\right) = 2 \left({r}^{3} + {5}^{3}\right)$

This reminds us of this polynomial identity : $\left({a}^{3} + {b}^{3}\right) = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right) \implies$

$2 \left({r}^{3} + {5}^{3}\right) = 2 \left(r + 5\right) \left({r}^{2} - 5 r + 25\right)$