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

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Answer 1 · 2015-04-12T07:22:07

To solve this, we will use the following property,

$A^3 + B^3= (A + B)(A^2 - B + B^2)$

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

Application:

$125x^3 + 169 = (5x)^3 + (169^(1/3))^3$

So $A = 5x$ and $B = 169^(1/3)$

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

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

So the final expression is
$= (5x + 169^(1/3))(25x^2 - 169^(1/3)x + 169^(2/3))$

How do you factor 125x^3 + 169125x^3 + 169??