Calculator
Example data table
| # | Pattern | Inputs (a,m,b,n,var) | Expression | Factored form |
|---|---|---|---|---|
| 1 | Difference of Squares | (3,1,2,1,x) | 9x2 − 4x2 | (3x − 2x)(3x + 2x) |
| 2 | Sum of Cubes | (2,1,1,1,t) | 8t3 + 1t3 | (2t + t)(4t2 − 2t2 + t2) |
| 3 | Difference of Cubes | (3,2,1,1,x) | 27x6 − 1x3 | (3x2 − x)(9x4 + 3x3 + x2) |
Examples show identity structure; your results may simplify further.
Formula used
- Difference of squares: A² − B² = (A − B)(A + B)
- Sum of cubes: A³ + B³ = (A + B)(A² − AB + B²)
- Difference of cubes: A³ − B³ = (A − B)(A² + AB + B²)
- Optional GCF: axᵐ ± bxⁿ = g·xᵏ(…)
How to use this calculator
- Select the binomial pattern that matches your expression.
- Enter A as a·xm and B as b·xn.
- Enable GCF to pull common factors out first.
- Press Factor Now to see the factored form.
- Download CSV or PDF to save your working.
FAQs
1) What binomials does this tool factor?
It factors difference of squares and sum or difference of cubes. It also can pull out a greatest common factor before applying identities.
2) What do a, b, m, and n mean?
A is a·xm and B is b·xn. The coefficients are a and b. The exponents are m and n for the chosen variable.
3) Why should I enable GCF first?
Many binomials simplify when you factor out common coefficients or powers of the variable. After that, the remaining binomial matches an identity more cleanly.
4) Can it handle negative exponents?
No. The calculator is designed for standard polynomial factoring. If you enter a negative exponent, it is treated as zero for stability.
5) Are results always fully simplified?
The tool outputs identity-based factors. Further simplification may be possible, such as combining like terms or simplifying inside factors, depending on your inputs.
6) Why do I see x in my result even if I chose another letter?
If the variable field is empty or invalid, the calculator defaults to x. Enter a single letter to keep your preferred variable consistent.
7) How do the download buttons work?
After factoring, use the CSV or PDF buttons to export your inputs, expression, final factorization, and steps. Files are generated instantly from your current result.