A polynomial in the form
a3 +
b3 is called a
sum of cubes. A polynomial in the form
a3 −
b3 is called a
difference of cubes.
Both of these polynomials have similar factored patterns:
A difference of cubes:
Example 1: Factor
x3 + 125.
Example 2: Factor 8
x3 − 27.
Example 3: Factor 2
x3 + 128
y3.
First find the GFC. GFC = 2
Example 4: Factor
x6 −
y6.
First, notice that
x6 −
y6 is both a difference of squares and a difference of cubes.
In general, factor a difference of squares before factoring a difference of cubes.