Just as the names suggest, a sum of cubes is an expression of the form:
a^{ 3} + b^{ 3},
and a difference of cubes is an expression of the form:
a^{ 3} − b^{ 3}.
A sum of cubes can be factored like this:
a^{ 3} + b^{ 3}
= (a + b)
(a^{ 2} − a b +
b^{ 2} ),
and a difference of cubes can be factored like this:
a^{ 3} − b^{ 3}
= (a − b)
(a^{ 2} + a b +
b^{ 2} ).
Notice the signs shown in red. The binomial on the right has the same sign
as the binomial on the left and the trinomial on the right has the opposite sign.
