Calculator
This tool simplifies polynomial-style algebraic expressions by expanding brackets, combining like terms, reducing rational coefficients, and sorting terms into a clean canonical form.
2x + 3x - 4, 3(x - 2) + x^2, 1/2x + 3/2x.
Example Data Table
| Input Expression | Simplified Output | What Changed |
|---|---|---|
| 2x + 3x - 4x + 7 | x + 7 | Like terms in x were combined. |
| 3(a + 2a) - 5a | 4a | Bracket expansion and term collection were applied. |
| 2(x + 3) - (x - 5) | x + 11 | Distributive expansion handled both brackets correctly. |
| x^2 + 3x^2 - x + 4 - 2 + 5x | 4x^2 + 4x + 2 | Quadratic, linear, and constant groups were merged. |
| 1/2x + 3/2x - 4 + 2(x - 1) | 4x - 6 | Fractional coefficients were reduced and combined. |
Formula Used
Core simplification rules
- Combine like terms: c₁m + c₂m + … + cₙm = (c₁ + c₂ + … + cₙ)m
- Distributive law: a(b + c) = ab + ac
- Subtract brackets: a - (b + c) = a - b - c
- Multiply variable powers: xᵐ · xⁿ = xᵐ⁺ⁿ
- Raise grouped terms: repeated multiplication is expanded under polynomial rules
- Divide by a nonzero constant: (cm) / k = (c / k)m
How the calculator organizes terms
A term is treated as a coefficient multiplied by a monomial pattern. Terms are considered like terms only when the variable letters and their powers match exactly.
After expansion, the calculator merges identical monomial patterns, reduces coefficients to lowest terms, and sorts the final expression by degree for a clear canonical result.
How to Use This Calculator
- Enter your expression using numbers, brackets, powers, and single-letter variables.
- Choose the graph variable and a numerical range if your expression uses one variable.
- Click Simplify Expression to expand, combine, and reorder the expression.
- Review the simplified answer, step summary, term table, and equivalence check.
- Use the CSV button for structured output or the PDF button for a printable report.
FAQs
1) What kinds of expressions does this calculator simplify?
It simplifies polynomial-style algebraic expressions with constants, fractions, brackets, multiplication, addition, subtraction, and nonnegative integer powers. It works best for school, tutoring, and algebra practice problems that focus on combining like terms and expanding brackets cleanly.
2) Does it show expanded expressions automatically?
Yes. Products and bracketed expressions are expanded during simplification. The final output is presented in canonical order so you can see the collected result rather than a partially expanded intermediate form.
3) Can I use fractions and decimals together?
Yes. Fractions like 1/2 and decimals like 0.75 are accepted. Coefficients are reduced internally, then displayed in a simplified rational form whenever possible.
4) Why is graphing sometimes unavailable?
Graphing is intended for constant or single-variable inputs. If your expression contains several variables, the page cannot draw a standard two-dimensional plot without fixing additional values first.
5) Does the calculator support implicit multiplication?
Yes. Inputs such as 2x, 3(x + 1), and xy are interpreted using implicit multiplication rules. For clarity, the internal parser makes those products explicit before simplification.
6) Can it divide by expressions like (x + 1)?
This version supports division by constants only. Division by variable expressions creates rational expressions, which need a different symbolic engine and separate simplification rules.
7) Why are terms reordered in the answer?
The calculator sorts terms by degree and variable pattern so the final form is easier to read and compare. This canonical order helps confirm equivalence across different but mathematically identical inputs.
8) What do the CSV and PDF buttons export?
CSV exports the original input, simplified output, summary metrics, and step notes in tabular text. PDF captures the visible result report so you can save or print the completed calculation.