Calculator
Supported format: one variable, parentheses, addition, subtraction, multiplication, constant division, and nonnegative integer powers up to 20.
Example Data Table
| Input expression | Simplified form | Degree | Value at x = 2 |
|---|---|---|---|
| (2x + 3x - 4) + x^2 | x^2 + 5x - 4 | 2 | 10 |
| (x + 2)(x - 3) + 4x | x^2 + 3x - 6 | 2 | 4 |
| 3(x^2 - 2x + 1) - (x^2 + x - 5) | 2x^2 - 7x + 8 | 2 | 2 |
| (2x - 1)^2 - (x^2 - 4x + 4) | 3x^2 - 3 | 2 | 9 |
| (x - 1)(x + 1)(x + 2) | x^3 + 2x^2 - x - 2 | 3 | 12 |
Formula Used
Canonical polynomial form: P(x) = Σ anxn
Combine like terms: axn + bxn = (a + b)xn
Multiply terms: (axm)(bxn) = abxm+n
Differentiate: d/dx [axn] = anxn-1
Evaluate at a point: P(v) = Σ anvn
This calculator first standardizes the expression, expands polynomial products and powers, then combines all matching exponents into one simplified result.
How to Use This Calculator
- Enter a polynomial-style expression such as (2x + 3)(x - 1).
- Choose the variable letter used inside the expression.
- Enter a value for direct evaluation after simplification.
- Set the decimal precision and graph range you want.
- Press Simplify Expression to show the result above the form.
- Review the canonical form, derivative, coefficients, and graph.
- Download the summary as CSV or PDF when needed.
FAQs
1. What kind of expressions does this calculator simplify?
It simplifies single-variable polynomial-style expressions using brackets, powers, addition, subtraction, multiplication, and division by constants. It expands products, combines like terms, and rewrites the result in descending powers.
2. Does it support multiple variables?
No. This version is designed for one variable at a time. That limitation keeps the parser dependable and makes the simplification, derivative, and graph sections easier to interpret.
3. Can I use implied multiplication like 2x or (x+1)(x-1)?
Yes. The calculator automatically inserts multiplication where it is clearly implied, so common textbook input styles work without forcing you to type every multiplication symbol.
4. Why does division only work with constants?
Division by another polynomial can create rational expressions rather than a simplified polynomial. This tool stays focused on polynomial simplification, so only constant denominators are accepted.
5. What happens when the expression becomes zero?
The output becomes 0, the degree is shown as 0, the derivative becomes 0, and the graph displays a flat line on the horizontal axis.
6. Why is there a derivative in a simplifier?
Many users simplify expressions before studying slope, turning points, or growth behavior. Showing the derivative adds practical value and helps connect algebraic cleanup with calculus ideas.
7. What does the graph represent?
The Plotly graph shows the simplified polynomial across your chosen x-range. It helps you inspect shape, intercept trends, symmetry, and fast growth without leaving the page.
8. Are the CSV and PDF files based on my result?
Yes. The downloads are created from the current output summary, including the original input, normalized form, simplified result, derivative, and key numeric details.