Solve expressions with GCF, grouping, and identities. Track steps, graph behavior, and save worked examples. Build confidence through clearer factoring workflows and reusable outputs.
Supported patterns include GCF, grouping, difference of squares, and perfect square trinomials.
The graph evaluates the original expression across sample x-values while other variables stay at 1.
| Expression | Factored Form | Method |
|---|---|---|
| 6x^2y+9xy^2 | 3xy(2x+3y) | GCF |
| x^2-4y^2 | (x-2y)(x+2y) | Difference of squares |
| x^2+2xy+y^2 | (x+y)^2 | Perfect square trinomial |
| ax+ay+bx+by | (a+b)(x+y) | Grouping |
1. Greatest common factor: Factor the largest common numeric and variable part from every term.
2. Grouping: Rearrange four-term expressions into two pairs, then factor each pair.
3. Difference of squares: a² − b² = (a − b)(a + b).
4. Perfect square trinomial: a² ± 2ab + b² = (a ± b)².
5. Variable exponent rule: Common variable factors use the smallest exponent shared by all terms.
Enter a polynomial with variables and exponents. Use forms like 6x^2y+9xy^2 or ax+ay+bx+by.
Press the factor button. The page shows the result above the form.
Review the step summary. It explains the recognized factoring method.
Use the graph to inspect expression behavior over sample x-values.
Download CSV for tabular results. Download PDF for a quick report.
It handles many structured multivariable polynomials. Supported methods include GCF extraction, four-term grouping, difference of squares, and perfect square trinomials.
No. Some expressions need advanced symbolic algebra systems. This page focuses on common educational factoring patterns and explains each detected step clearly.
Use the caret symbol. Write x^2y^3 instead of superscripts. Keep multiplication implied, such as 4xy or 7ab^2.
Grouping succeeds when each pair shares a factor and both pairs reduce to the same remaining binomial. Then that shared binomial becomes a common factor.
The graph samples the original polynomial by changing x from -5 to 5. Other variables stay fixed at 1 for quick visual comparison.
The exported table compares sampled values for study use. Exact symbolic evaluation of every formatted factor form may require a full symbolic parser.
Yes. It is useful for homework checks, pattern recognition, worked examples, and introductory algebra practice involving several variables and exponents.
First, verify your input syntax. Then check whether the polynomial is already irreducible under these supported patterns or needs a more advanced factoring method.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.