Multiplying Polynomials Calculator

Enter two polynomials in Polynomial A and Polynomial B fields — the Multiplying Polynomials Calculator distributes every term across both expressions, combines like terms, and returns the fully expanded and simplified result. Supports expressions up to degree 6 with real coefficients, including binomials, trinomials, and beyond.

Enter using ^ for exponents (e.g. x^2), standard +/- signs, and real coefficients.

Enter the second polynomial the same way (e.g. 2x^3 - x + 5).

Results

Expanded & Simplified Result

--

Degree of Polynomial A

--

Degree of Polynomial B

--

Degree of Result

--

Number of Terms in Result

--

Coefficient by Degree in Result Polynomial

Results Table

Frequently Asked Questions

How do you multiply two polynomials?

Polynomial multiplication uses the distributive property: every term in the first polynomial is multiplied by every term in the second polynomial. After expanding all products, you collect and combine like terms (those sharing the same exponent) to produce the simplified result.

What is the FOIL method and when does it apply?

FOIL stands for First, Outer, Inner, Last — it is a memory device for multiplying two binomials. For example, (a + b)(c + d) = ac + ad + bc + bd. FOIL is a specific case of the general distributive property and only applies directly when both expressions have exactly two terms.

What degree is the result when multiplying two polynomials?

The degree of the product equals the sum of the degrees of the two polynomials. For example, multiplying a degree-2 polynomial by a degree-3 polynomial yields a degree-5 result.

Can I multiply polynomials with more than two terms?

Yes. The distributive property applies regardless of how many terms each polynomial contains. A trinomial times a trinomial, for instance, produces up to 9 partial products before combining like terms. This calculator handles expressions up to degree 6.

How do I enter polynomials into the calculator?

Type each polynomial using standard notation: use ^ for exponents (e.g. x^2), * or nothing for implied multiplication, and + or - to separate terms. For example, enter 3x^2 + 2x - 1 for the first polynomial and x - 4 for the second.

What happens to like terms when multiplying polynomials?

After distributing all term-by-term products, any two terms with the same exponent are combined by adding their coefficients. This simplification step reduces the number of terms and produces the final, compact polynomial.

Does the order of the two polynomials matter?

No. Polynomial multiplication is commutative: A × B and B × A produce identical results. The order you enter them into the calculator does not affect the expanded and simplified output.

What is the difference between expanding and simplifying a polynomial product?

Expanding means writing out all the individual term-by-term products without combining anything. Simplifying (or collecting like terms) then adds together all terms that share the same degree, reducing the expression to its minimal form. This calculator shows the fully simplified result.

More Math Tools