Question

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

Answer 1

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))`