Difference of Cubes Calculator
Factor a³ − b³ and a³ + b³ step by step.
Enter your values
Enter the a you are working with.
Enter the b you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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.
What do I need to enter into the Difference of Cubes Calculator?
Just 2 values: a, b. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Difference of Cubes Calculator work out the answer?
The difference of cubes factors as a³ − b³ = (a − b)(a² + ab + b²); the sum of cubes uses (a + b)(a² − ab + b²). It applies the formula a³ − b³ = (a − b)(a² + ab + b²) and shows the working so you can check each step by hand.
Is the Difference of Cubes Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.