# How do you factor 125x^3 + 169??

Apr 12, 2015

To solve this, we will use the following property,

${A}^{3} + {B}^{3} = \left(A + B\right) \left({A}^{2} - B + {B}^{2}\right)$

Verify it and you'll see that it's true.

Application:

$125 {x}^{3} + 169 = {\left(5 x\right)}^{3} + {\left({169}^{\frac{1}{3}}\right)}^{3}$

So $A = 5 x$ and $B = {169}^{\frac{1}{3}}$

=> (5x)^3 + (169^(1/3))^3 = (5x + 169^(1/3))((5x)^2 - 169^(1/3)x + (169^(1/3))^2

Pay close attention, for this formula can be quite tricky at times!

So the final expression is
$= \left(5 x + {169}^{\frac{1}{3}}\right) \left(25 {x}^{2} - {169}^{\frac{1}{3}} x + {169}^{\frac{2}{3}}\right)$