How do you factor 199b^3-133b?

Jun 3, 2016

$199 {b}^{3} - 133 b = b \left(\sqrt{199} b - \sqrt{133}\right) \left(\sqrt{199} b + \sqrt{133}\right)$

Explanation:

The difference of squares identity can be written:

${A}^{2} - {B}^{2} = \left(A - B\right) \left(A + B\right)$

First note that $199 {b}^{3}$ and $133 b$ are both divisible by $b$, so separate that out as a factor first...

$199 {b}^{3} - 133 b$

$= b \left(199 {b}^{2} - 133\right)$

$= b \left({\left(\sqrt{199} b\right)}^{2} - {\left(\sqrt{133}\right)}^{2}\right)$

$= b \left(\sqrt{199} b - \sqrt{133}\right) \left(\sqrt{199} b + \sqrt{133}\right)$