Factor the Sum of Two Cubes: a3 + b3

How to factor the sum of two cubes, a3 + b3: formula, 1 example, and its solution.

Formula

Formula

a3 + b3 = (a + b)(a2 - ab + b2)

The sign of +b3 is plus.
Then the sign in (a + b) is plus.
And the sign of -ab is minus.

Example

Example

Solution

Change x3 + 8 to the sum of two cubes.

x3 is x3.
+8 is +23.

x3 + 23 is the sum of two cubes.
So x3 + 23 = (x + 2)(x2 - x⋅2 + 22).

+23 is plus.
So the sign in (x + 2) is plus.
And the sign of -x⋅2 is minus.

-x⋅2 = -2x
+22 = +4

So (x + 2)(x2 - 2x + 4) is the answer.