Sum and Difference of Cubes

Factors sums and differences of perfect cubes.

a^{3} \pm b^{3} = (a \pm b) (a^{2} \mp ab + b^{2})

Variables

Remember SOAP for the signs: Same, Opposite, Always Positive. The quadratic factor $a^{2} \mp ab + b^{2}$ never factors further over the reals.

$x^{3} - 8 = (x - 2) (x^{2} + 2 x + 4)$ .

Factor polynomials completely: GCF, trinomials, difference of squares, sum of cubes and higher-degree polynomials.

Difference of Squares

Factors the difference of two perfect squares.