Difference of Cubes Calculator
Factor a³ − b³ and a³ + b³ step by step.
Enter your values
Results update instantly as you type — no submit needed.
Results
- Difference a³ − b³
- 117
- Factored form
- (5 − 2)(a² + ab + b²) = (5 − 2)(39)
- Sum a³ + b³
- 133
- Sum factored
- (5 + 2)(19)
Working
- 1a³ = 125
- 2b³ = 8
- 3a² + ab + b² = 39
Quick answer
The difference of cubes factors as a³ − b³ = (a − b)(a² + ab + b²); the sum of cubes uses (a + b)(a² − ab + b²).
a³ − b³ = (a − b)(a² + ab + b²)
At a glance
| What it does | Factor a³ − b³ and a³ + b³ step by step. |
|---|---|
| Category | Math |
| Inputs needed | a, b |
| Main output | Difference a³ − b³ |
| Formula | a³ − b³ = (a − b)(a² + ab + b²) |
| Cost | Free — no sign-up, no download |
How to use the Difference of Cubes Calculator
- 1Enter the cube root a of the first term.
- 2Enter the cube root b of the second term.
- 3Read the factored form and the numeric check.
Inputs explained
- a
- Enter the a you are working with.
- b
- Enter the b you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- a5
- b2
Results
- Difference a³ − b³117
- Factored form(5 − 2)(a² + ab + b²) = (5 − 2)(39)
- Sum a³ + b³133
- Sum factored(5 + 2)(19)
- a³ = 125
- b³ = 8
- a² + ab + b² = 39
Frequently asked questions
How do you factor a difference of cubes?
Write (a − b) times the 'SOAP' trinomial a² + ab + b²; the trinomial never factors further over the reals.
What does SOAP stand for?
Same, Opposite, Always Positive — the sign pattern for the binomial and trinomial factors.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.