# Factor the Sum of Two Cubes: a^{3} + b^{3}

How to factor the sum of two cubes, a^{3} + b^{3}: formula, 1 example, and its solution.

## Formula

### Formula

a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})

The sign of +b^{3} is plus.

Then the sign in (a + b) is plus.

And the sign of -ab is minus.

## Example

### Example

### Solution

Change x^{3} + 8 to the sum of two cubes.

x^{3} is x^{3}.

+8 is +2^{3}.

x^{3} + 2^{3} is the sum of two cubes.

So x^{3} + 2^{3} = (x + 2)(x^{2} - x⋅2 + 2^{2}).

+2^{3} is plus.

So the sign in (x + 2) is plus.

And the sign of -x⋅2 is minus.

-x⋅2 = -2x

+2^{2} = +4

So (x + 2)(x^{2} - 2x + 4) is the answer.