The calculator applies core algebraic rules to convert an input into a simplified polynomial-style expression. It first rewrites implicit multiplication, then expands powers and products, and finally merges like terms.
General model: aX + bX = (a + b)X
Product rule: (aX)(bY) = (ab)(XY)
Power rule: (X)n multiplies the same factor repeatedly for nonnegative integer exponents.
Distributive rule: a(b + c) = ab + ac
Like-term condition: Two terms combine only when their variable part and exponents match exactly.
- Enter an algebraic expression using numbers, variables, parentheses, and powers.
- Use forms like
2x,3(x+1), or(x-2)^2. - Set the variable order if you want a custom display style.
- Choose the number of decimal places for coefficient rounding.
- Select a sorting method to order the final terms.
- Press Simplify Expression to view the result above the form.
- Review the result table, graph, and optional steps.
- Use the CSV and PDF buttons to export the current output.
| Input Expression | Simplified Output | Detected Variables | Highest Degree |
|---|---|---|---|
2x + 5x - 3 |
7x - 3 |
x | 1 |
(x + 2)(x - 2) |
x^2 - 4 |
x | 2 |
3ab + 2ab - b + b |
5ab |
a, b | 2 |
(x - 1)^2 + 2x |
x^2 + 1 |
x | 2 |
1. What kinds of expressions can this calculator simplify?
It simplifies polynomial-style expressions with numbers, variables, parentheses, multiplication, addition, subtraction, and nonnegative integer powers. It also understands implicit multiplication such as 2x and 3(x+1).
2. Does it combine like terms automatically?
Yes. Terms are combined when their variable part matches exactly, including all exponents. For example, 4x² and -x² become 3x², but 4x and 4x² stay separate.
3. Can it expand brackets and powers?
Yes. The engine expands products and repeated factors such as (x+2)(x-2) and (x-1)^3, then combines the resulting like terms into a cleaner expression.
4. Does the calculator support multiple variables?
Yes. You can simplify expressions with variables such as x, y, z, a, or b. It can manage multivariable terms like 3xy, 2x²y, and 5ab².
5. Why do some terms not combine?
Terms combine only when their variable pattern is identical. A different exponent or different variable set creates a different term, so x²y and xy² remain separate.
6. What does the graph show?
The Plotly graph summarizes the structure of your expression. It compares input terms, simplified terms, detected variables, and highest degree so you can review complexity quickly.
7. What is included in the CSV and PDF exports?
The exports capture the current result summary and the simplified term table. They help you save a working example, share results, or attach them to notes and assignments.
8. Is this useful for homework checking?
Yes. It is useful for classroom review, self-checking, and quick verification of algebra steps. The optional step section helps show how the expression was normalized and simplified.