Multiply Polynomials Calculator

Enter two polynomials and get the expanded product — with every distribution step shown, so you can follow (and learn) the working.

First polynomial

Second polynomial

Use ^ for powers and a single variable, e.g. 3x^2 - 5x + 2. The variable can be any letter.

🔒 Everything is computed in your browser — nothing is uploaded.

🔒 Nothing you enter is sent anywhere or stored. All processing happens in your browser.

Features

Full expanded product

Enter two polynomials and get the multiplied-out result in standard form, highest power first — not just binomials, any length.

Step-by-step working

See every term-by-term product before they're combined, so you can follow the FOIL/distribution method and check your own work.

Any single variable, any power

Handles x, y, or any letter, with whole-number exponents and positive, negative, whole or decimal coefficients.

Instant and private

It solves as you type and runs entirely in your browser — nothing is uploaded, and it works offline.

How it works — in four simple steps

No signup, nothing to install — it all runs in your browser.

Step 01

Enter the first polynomial

Type it with ^ for powers, e.g. 2x^2 + 3x - 1. Any single variable works.

Step 02

Enter the second polynomial

Type the polynomial you're multiplying by, using the same variable.

Step 03

Multiply

Press Multiply to see the expanded product in standard form.

Step 04

Show the steps

Press Show steps to reveal every distribution before the like terms are combined.

How it works

Multiplying polynomials means multiplying every term of the first by every term of the second, then adding up (combining) the like terms — the terms with the same power of the variable. For two binomials this is the familiar FOIL method (First, Outer, Inner, Last); for longer polynomials it's the same idea, just with more products.

This calculator parses both polynomials, distributes each pair of terms, and combines the results into a single expanded polynomial in standard form (highest power first). Press Show steps to see every individual product before they're combined, which makes it a useful check for homework rather than a black box.

It works with a single variable to any whole-number power, with positive or negative and whole or decimal coefficients. Everything runs in your browser — nothing is uploaded.

Examples

(x + 2)(x + 3) → x² + 5x + 6

(2x² + 3x − 1)(x − 4) → 2x³ − 5x² − 13x + 4

(x − 1)(x + 1) → x² − 1 (difference of squares)

Frequently asked questions

How do you multiply two polynomials?

Multiply each term of the first polynomial by each term of the second, then add together the terms with the same power (like terms). For two binomials this is the FOIL method; the calculator does it for polynomials of any length.

What is the FOIL method?

FOIL — First, Outer, Inner, Last — is a way to remember the four products when multiplying two binomials, e.g. (x+2)(x+3). It's just the distributive law; this tool extends the same idea to longer polynomials.

Can it handle powers and negative coefficients?

Yes. Use ^ for exponents (whole numbers ≥ 0) and a minus sign for negatives, e.g. -3x^2 + 5x - 1. Decimal coefficients work too.

Does it show the working?

Yes — press Show steps to see every term-by-term product laid out before they're combined into the final answer, so you can check each stage.

Is it free and private?

Yes. It's free, needs no signup, and computes everything in your browser, so nothing you enter is uploaded.