Multiplying Polynomials Calculator

Multiply polynomials step by step

The calculator will multiply two polynomials (quadratic, binomial, trinomial, etc.), with steps shown.

First polynomial:

Second polynomial:

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Welcome to the intuitive and user-friendly Multiplying Polynomials Calculator. This advanced tool simplifies multiplying two polynomials, removing manual calculations and ensuring you get the most accurate results.

How to Use the Multiplying Polynomials Calculator?

  • Input

    Enter the polynomials you wish to multiply in the provided fields. Ensure you follow the accepted format, typically using variables like $$$x$$$ or $$$y$$$.

  • Calculation

    After entering the polynomials, click the "Calculate" button.

  • Result

    The calculator will instantly calculate the product of the entered polynomials.

What Is a Polynomial?

A polynomial is a mathematical expression consisting of a sum of terms, where each term is the product of a constant and a variable raised to a non-negative integer exponent. In simpler terms, a polynomial combines constants, variables, and exponents using addition, subtraction, and multiplication.

The highest power of the variable in the polynomial determines the degree of a polynomial.

For instance, consider the following polynomial:


In this polynomial:

  • $$$4x^3$$$, $$$-5x^2$$$, $$$7x$$$, and $$$-8$$$ are the terms.
  • $$$x$$$ is the variable.
  • $$$3$$$, $$$2$$$, and $$$1$$$ are the exponents corresponding to their terms.
  • $$$4$$$, $$$-5$$$, $$$7$$$, and $$$-8$$$ are the coefficients of the terms.
  • The degree of this polynomial is $$$3$$$ because the highest power of the variable $$$x$$$ is $$$3$$$.

Polynomials can have one or more terms. For example:

  • $$$5x^2$$$ is a monomial (one term).
  • $$$3x-7$$$ is a binomial (two terms).
  • $$$x^2-3x+4$$$ is a trinomial (three terms).
  • $$$x^3+2x^2-4x+1$$$ is a polynomial with four terms.

Polynomials can represent various mathematical and real-world situations, from simple equations to complex models.

How to Multiply Polynomials?

Multiplying polynomials involves multiplying each term of the first polynomial by each term of the second polynomial, combining like terms and simplifying the result. Here's a step-by-step approach to multiplying polynomials:

  • Distribute Each Term: Start by taking each term of the first polynomial and multiplying it by each term in the second polynomial.
  • Apply the Exponent Rules: When multiplying two powers of the same base, you add their exponents. For instance, $$$x^ax^b=x^{a+b}$$$.
  • Combine Like Terms: After distributing, some terms might have the same variable raised to the same power. Combine these terms by adding or subtracting their coefficients.
  • Simplify: Once you've combined all like terms, write down the polynomial in standard form, which means arranging the terms in descending order of their degree.

As an example, multiply the binomials $$$x+2$$$ and $$$x-3$$$:

  1. Start by multiplying the first term of the first binomial $$$(x)$$$ by both terms of the second binomial:

    $$x\cdot x=x^1x^1=x^{1+1}=x^2$$$$x\cdot(-3)=-3x$$
  2. Now, multiply the second term of the first binomial $$$(2)$$$ by both terms of the second binomial:

    $$2\cdot x=2x$$$$2\cdot(-3)=-6$$
  3. Combine all the results:

  4. Combine like terms:


So, $$$(x+2)(x-3)=x^2-x-6$$$.

The process would be similar for polynomials with more terms, ensuring each term of the first polynomial is multiplied by each term of the second polynomial.

Why Choose Our Multiplying Polynomials Calculator?

  • Precision and Accuracy

    Our calculator ensures that each multiplication is performed precisely, eliminating potential human errors.

  • Efficiency

    Save valuable time! Instead of manually multiplying term-by-term and possibly overlooking like terms, our calculator presents results instantly.

  • User-Friendly Interface

    Designed with user experience in mind, the interface is intuitive and straightforward, making polynomial multiplication a breeze, even for first-timers.

  • Versatility

    Whether multiplying binomials, trinomials, or higher-degree polynomials, our calculator is versatile enough to handle them all.


What is a polynomial?

A polynomial is a mathematical expression involving variables and coefficients. It is composed of terms. They are formed by multiplying constants by variables raised to non-negative integer exponents.

How does this calculator work?

The Multiplying Polynomials Calculator takes two polynomials as input and finds their product, presenting the result in its simplest form.

What is the use of polynomials in real life?

Polynomials have numerous applications in real life. They are used in physics for modeling trajectories, engineering for determining structural loads, economics for forecasting trends, and many other fields. Additionally, polynomial functions help us understand and interpret various phenomena and patterns we see in nature and everyday life.

How do you multiply polynomials using the vertical method?

The vertical method of multiplying polynomials is similar to the traditional method of multiplying numbers.