Expand algebraic forms with steps, terms, and checks. Study products, powers, patterns, and clean symbolic results today.
Choose the expansion mode first. Use binomial mode for expressions like (ax + b)n. Use product mode for two polynomials. Use power mode for repeated multiplication of one polynomial.
Enter a single variable symbol. Add an optional value to test the final expansion numerically. The result appears above the form after submission.
For product mode, write expressions without spaces if you prefer. Examples include 3x^2+2x-5, x-4, and x^3+1. The parser accepts positive and negative terms.
Use the CSV button to save the term table. Use the PDF button for a clean report. The graph plots the expanded polynomial across a fixed interval.
For a binomial expression, the standard rule is:
(ax + b)n = Σ [ C(n,k) × (ax)n-k × bk ] for k from 0 to n.
Here, C(n,k) is the combination value. It equals n! / (k!(n-k)!). This gives every term coefficient before like terms are combined.
Each term in the first polynomial multiplies every term in the second polynomial. Coefficients multiply directly. Exponents of the same variable add together.
(cxm)(dxn) = (cd)xm+n
A polynomial power is found by repeated multiplication. For example, (P(x))3 = P(x) × P(x) × P(x). The calculator handles the repeated products automatically.
| Input Type | Expression | Expanded Result |
|---|---|---|
| Binomial Power | (2x + 3)^3 | 8x^3 + 36x^2 + 54x + 27 |
| Product | (x + 2)(x - 5) | x^2 - 3x - 10 |
| Power | (x^2 + x + 1)^2 | x^4 + 2x^3 + 3x^2 + 2x + 1 |
Variable expansion builds algebra fluency. Students use it to simplify expressions, compare coefficients, solve equations, and verify symbolic patterns. It also supports calculus, linear algebra, statistics, and discrete mathematics.
Expanding an expression shows structure. You can see degree, leading coefficient, constant term, and symmetry. Those details help with graph shape, roots, and growth trends.
Teachers often use expansion to explain distributive thinking. It connects arithmetic patterns with abstract symbols. That link improves accuracy when learners move into advanced topics.
This calculator also acts as a checking tool. You can compare manual work with an exact computed result. Step output helps identify sign mistakes and missed like terms.
The graph adds a second view. Symbolic output shows algebraic form, while the curve shows behavior over a range. Together they support stronger mathematical understanding.
It expands binomial powers, multiplies two polynomials, and raises one polynomial to a positive integer power. It works for single-variable algebraic expressions.
Use forms like 2x^2+3x-4, x-7, or x^3+2x+1. A single letter variable works best. Avoid brackets inside the polynomial text fields.
Yes. After multiplication or power expansion, it merges terms with the same exponent and displays the simplified polynomial.
Yes. Enter any numeric value in the evaluation field. The calculator then computes the expanded expression at that point.
Large powers create many terms and slower processing. Reasonable limits keep the calculator fast, readable, and stable for everyday mathematical work.
The graph plots the final expanded polynomial over a fixed x-range. It helps you inspect turning behavior, sign changes, and growth direction.
The CSV file includes exponent, coefficient, and formatted term values. It is useful for records, worksheets, or follow-up analysis.
No. This version is designed for one-variable expansions. Multi-variable symbolic algebra needs a more advanced parser and term management system.
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.