Polynomial Multiplication Calculator
Multiply polynomials online
How to multiply polynomials (2026 tips)
Follow the distributive property (every term in A × every term in B) and combine like terms. Use the FOIL method for binomials, or the box method for larger ones. This calculator automates the process and shows each cross multiplication.
Box method in action
Write one polynomial along the top, the other down the left. Fill each cell by multiplying row × column. Then add all cells — this is exactly how our calculator tabulates multiplication. Great for visual learners!
Checklist for success: ✅ Align like terms ✅ Combine signs ✅ Reduce exponents correctly ✅ Verify with our calculator.
Quick reference: common polynomial products
| Expression 1 | Expression 2 | Product (simplified) |
|---|---|---|
| (x + a)(x + b) | binomial × binomial | x² + (a+b)x + ab |
| (x + a)² | square of binomial | x² + 2ax + a² |
| (ax + b)(cx + d) | general binomial | ac x² + (ad+bc)x + bd |
| (x² + 2x + 1)(x-1) | trinomial × binomial | x³ + x² - x -1 |
| (x² - 1)(x² + 1) | difference of squares | x⁴ - 1 |
⭐ Use our calculator to verify your homework or prepare for AP / college algebra exams 2026.
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Frequently asked questions
It's an online tool that multiplies two polynomials and shows each intermediate product, combining like terms and displaying final simplified expression.
The box method arranges polynomial terms in a grid, multiplies row×column, and sums the results — our calculator visualizes this grid automatically.
Yes! Multiply factors (x - zero)^multiplicity to construct the polynomial. Our tool helps you verify the expanded form.
Currently optimized for single variable (x). For multiple variables, we recommend the distributive property manually, but upcoming upgrades will include multivariable.
Absolutely. 100% free, no signup, updated with accurate exponent handling — perfect for SAT, AP, and college algebra.
LCM of polynomials is the smallest polynomial divisible by both. While this tool focuses on multiplication, you can factor polynomials and combine LCM using multiplication of unique factors.