Calculator Inputs
Use the factor switches to include up to three linear factors. Each active factor follows the form (ax + b)p.
Example Data Table
| Multiplier | Factor 1 | Factor 2 | Factor 3 | Evaluate At | Expanded Result |
|---|---|---|---|---|---|
| 1 | (2x + 3)2 | (x - 4)1 | Disabled | x = 2 | 4x3 - 4x2 - 39x - 36 |
| -2 | (x + 1)3 | (3x - 2)1 | (x + 5)1 | x = 1 | -6x5 - 26x4 - 16x3 + 32x2 + 14x + 20 |
Formula Used
The calculator expands a product of powered linear factors using repeated polynomial multiplication.
- Each active factor is written as (ax + b)p.
- A power is expanded by multiplying the same linear factor by itself p times.
- Two polynomials are multiplied by combining like powers: (cᵢxi)(dⱼxj) = cᵢdⱼxi+j.
- Like terms are added to produce the final simplified polynomial.
- The derivative is found using d/dx [cxn] = ncxn-1.
- The antiderivative is found using ∫ cxn dx = cxn+1 / (n+1) + C.
How to Use This Calculator
- Enter the variable symbol, global multiplier, evaluation point, and graph range.
- Enable one, two, or three factors.
- For each active factor, enter the linear coefficient, constant term, and exponent.
- Press Expand Polynomial to display the simplified polynomial above the form.
- Review the derivative, antiderivative, coefficient table, and graph.
- Use the export buttons to save the coefficient table as CSV or the full results as PDF.
FAQs
1. What kind of expressions can this calculator expand?
It expands up to three powered linear factors, each shaped like (a x + b)p, with an optional overall multiplier. This covers many classroom and exam-style polynomial products.
2. Can I use decimal coefficients?
Yes. The calculator accepts integers and decimals for every coefficient, constant, graph bound, and evaluation input. Results are formatted cleanly without unnecessary trailing zeros.
3. Does it combine like terms automatically?
Yes. Every multiplication step adds coefficients sharing the same power, so the final answer appears as a simplified polynomial rather than a partially expanded expression.
4. Why is the derivative included?
The derivative helps you study slope, turning behavior, and rate of change after expansion. It is useful for algebra, calculus preparation, and graph interpretation.
5. What does the coefficient table show?
It lists each polynomial degree beside its coefficient. This table makes it easier to verify terms, export data, and reuse coefficients in other math tools.
6. Can I plot the expanded polynomial?
Yes. The Plotly graph uses your selected x-range and graph points to draw the polynomial curve, helping you see growth, intercept tendencies, and symmetry patterns.
7. What happens if an exponent is zero?
Any active factor raised to zero becomes 1, so it does not change the final polynomial. This follows the standard exponent rule for nonzero expressions.
8. What can I export from this calculator?
You can export the coefficient table as a CSV file and save the result section as a PDF. Both exports work after a successful expansion.