# How do you factor -375a^3 + 648?

Sep 25, 2015

$3 \left(6 - 5 a\right) \left(36 + 30 a + 25 {a}^{2}\right)$

#### Explanation:

To factorise, we can try to put into the shape of difference of cubes, to see if this can help. Accordingly,

$- 375 {a}^{3} + 648 = 3 \left(216 - 125 {a}^{3}\right)$

=$3 \left({6}^{3} - {5}^{3} {a}^{3}\right)$

= $3 \left(6 - 5 a\right) \left({6}^{2} + 6 \cdot 5 a + {5}^{2} {a}^{2}\right)$

=$3 \left(6 - 5 a\right) \left(36 + 30 a + 25 {a}^{2}\right)$