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

1 Answer
Apr 12, 2015

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))#