Kevin S. answered • 03/13/13

The sum of two cubes a^{3}x^{3} + c^{3} can be factored as

(ax + c) (a^{2}x^{2} - acx + c^{2})

The difference of two cubes a^{3}x^{3} - c^{3} can be factored as

(ax - c) (a^{2} x^{2} + acx + c^{2})

So the sign between the cubes goes with the linear factor, the opposite sign goes between the 2nd degree term and the linear term in the quadratic factor, and the sign in front of the constant (in the quadratic factor) will always be positive.