Expansion of Polynomial Products Calculator

Enter several polynomials and inspect every product coefficient. Compare curves, tables, exports, and algebra summaries. Build reliable practice with fast structured calculator output today.

Calculator form

Enter each polynomial in its own field. Leave unused fields empty.

Accepted examples: x^2+2x+1, -3x^3+0.5x-4, x-1, 2.

Polynomial 1

Polynomial 2

Polynomial 3

Polynomial 4

Decimal precision

Evaluate product at x

Graph minimum x

Graph maximum x

Graph sample points

Formula used

Polynomial form

If P(x) = Σ a_ixⁱ and Q(x) = Σ b_jx^j, then:

P(x)Q(x) = Σ c_kx^k, where c_k = Σ a_ib_j for all pairs with i + j = k.

The calculator applies the distributive law across every input polynomial. It multiplies coefficients, adds exponents, and combines like powers into one final simplified expansion.

For three or four factors, the same convolution rule repeats stage by stage until one final product remains.

How to use this calculator

Type at least two polynomials into the input fields.
Use x as the variable and write exponents with ^.
Leave unused polynomial boxes empty.
Set your preferred rounding precision and graph range.
Choose an x-value if you want a numeric evaluation.
Press Expand Product to see the result above the form.
Review the stepwise multiplication, table, and graph.
Use the export buttons to save CSV or PDF reports.

Example data table

Polynomial 1	Polynomial 2	Polynomial 3	Expanded product	Value at x = 2
x + 1	x - 1	x + 2	x³ + 2x² - x - 2	12
x² + 2x + 1	x² - x + 3	—	x⁴ + x³ + 2x² + 5x + 3	37
2x - 3	x² + 4	x + 5	2x⁴ + 10x³ - 3x² - 7x - 60	18

Frequently asked questions

1. What input format should I use?

Use one polynomial per field. Write terms like x^2, -3x, 4, or 0.5x^3. Spaces are optional. Parentheses around each whole polynomial are also fine.

2. Can I multiply more than two polynomials?

Yes. This page accepts up to four polynomial factors. Empty fields are ignored, so you can use two, three, or four valid inputs.

3. Does the calculator combine like terms automatically?

Yes. After distribution, it groups all matching exponents and adds their coefficients. The final output is shown in simplified polynomial form.

4. Can I use decimals in coefficients?

Yes. Decimal coefficients such as 0.5x^2 or -1.25x are supported. The precision setting controls how many decimals appear in the displayed results.

5. What does the graph show?

The graph plots every entered polynomial and the final expanded product across your chosen x-range. It helps you compare shapes and zeros visually.

6. What is the coefficient table for?

It lists each exponent with its final coefficient. This is useful for checking term order, copying values into notes, or exporting clean algebra data.

7. What happens if one polynomial is constant?

A constant still works as a polynomial. It scales every coefficient in the product by that constant and keeps the polynomial structure intact.

8. Why is evaluation at x useful?

Evaluation gives one numeric output for the expanded product at a chosen x-value. It is handy for checking substitutions and comparing equivalent expressions.