FOIL stands for First, Outer, Inner, Last—a way to multiply two binomials. For (a+b)(c+d): First=ac, Outer=ad, Inner=bc, Last=bd. Sum all terms.

How do you multiply larger polynomials?

Use the distributive property: multiply each term in the first polynomial by every term in the second, then combine like terms.

What degree is the product of two polynomials?

The degree of the product equals the sum of the degrees. A degree 2 polynomial times a degree 3 polynomial gives degree 5.

Terms with identical variable parts. You can only combine like terms: 3x² + 5x² = 8x², but 3x² + 5x cannot be combined.

Multiplying Polynomials Calculator

Multiply polynomials step-by-step using FOIL and distributive property. See each term multiplied and combined.

First Polynomial

Second Polynomial

Input format: Use x for variable, ^ for exponents. Examples: x^2, 2x + 1, -3x^2 + 4x - 5

Try These Examples

FOIL Method (for Binomials)

First terms

Outer terms

Inner terms

Last terms

(a + b)(c + d) = ac + ad + bc + bd

Example: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6

Special Product Patterns

Difference of Squares

(a + b)(a - b) = a² - b²

Perfect Square (Sum)

(a + b)² = a² + 2ab + b²

Perfect Square (Difference)

(a - b)² = a² - 2ab + b²

Related Math Tools

About Multiplying Polynomials Calculator - FOIL & Beyond

Multiply polynomials with step-by-step solutions. FOIL method, binomials, trinomials, and higher degree polynomial multiplication.

Our **Multiplying Polynomials Calculator** multiplies any two polynomials with detailed step-by-step solutions. From simple binomials (FOIL) to complex higher-degree polynomials, get organized, simplified results. See also our Distributive Property Calculator.

Polynomial multiplication uses the distributive property to multiply each term in the first polynomial by each term in the second. Our calculator organizes these products, combines like terms, and presents the final expanded form.

Perfect for algebra students learning FOIL, calculus preparation, and anyone working with polynomial expressions. Understand the multiplication process through our clear step-by-step explanations.

Key Features

FOIL method display

Any degree polynomials

Like term combination

Step-by-step process

Organized output

Educational format

Why Use This Tool?

Master FOIL method

Understand distribution

Algebra homework help

Exam preparation

Quick verification

Common Use Cases

Algebra: Multiply binomials and trinomials.

Calculus: Expand expressions for differentiation.

Factoring: Verify factorization by multiplying.

Equations: Expand to solve polynomial equations.

Related Tools

Distributive Property Calculator

Expand single distributions.

Rational Expressions Calculator

Fraction operations.

How to Use

Enter first polynomial coefficients

Enter second polynomial coefficients

Click Multiply

View product and detailed steps