# How do you factor completely 16x^3-32x^2-25x+50?

Apr 26, 2016

$16 {x}^{3} - 32 {x}^{2} - 25 x + 50 = \left(4 x - 5\right) \left(4 x + 5\right) \left(x - 2\right)$

#### Explanation:

Factor by grouping, then using the difference of squares identity:

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

with $a = 4 x$ and $b = 5$ as follows:

$16 {x}^{3} - 32 {x}^{2} - 25 x + 50$

$= \left(16 {x}^{3} - 32 {x}^{2}\right) - \left(25 x - 50\right)$

$= 16 {x}^{2} \left(x - 2\right) - 25 \left(x - 2\right)$

$= \left(16 {x}^{2} - 25\right) \left(x - 2\right)$

$= \left({\left(4 x\right)}^{2} - {5}^{2}\right) \left(x - 2\right)$

$= \left(4 x - 5\right) \left(4 x + 5\right) \left(x - 2\right)$