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Enter your polynomials

Use one variable letter (like x), ^ for exponents, and +/− signs. Example: -3x^2 + x - 7

Parentheses are optional; they’re ignored if present. Example: (x-5)

This calculator supports single-variable polynomials. Use the same variable letter in both inputs (common choices: x, y, t).

Options:

Result:

No results yet. Enter polynomials and click Calculate.

How to use this calculator

  • Enter the two polynomials in Polynomial A and Polynomial B.
  • Click Calculate to get expanded and simplified results.

How this calculator works

  • Parse each polynomial into terms like ax^n.
  • Distribute: multiply A by each term in B.
  • Combine like terms (same exponent) to simplify.

Formula & Equation Used

Polynomial multiplication uses the distributive property:

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

More generally, multiply every term in the first polynomial by every term in the second polynomial:

(aₘxᵐ + … + a₁x + a₀)(bₙxⁿ + … + b₁x + b₀)

Then add all term-by-term products and combine like terms.

Example Problems & Step-by-Step Solutions

Example 1 — Binomial × Binomial

Multiply (x + 2)(x + 5).

Step-by-step

  1. Distribute: (x + 2)(x + 5) = x(x + 5) + 2(x + 5)
  2. Multiply: = (x^2 + 5x) + (2x + 10)
  3. Combine like terms: x^2 + 7x + 10

Answer: x^2 + 7x + 10

Tip: This is the classic FOIL case.

Example 2 — Trinomial × Binomial

Multiply (x^2 + 2x + 1)(x − 3).

Step-by-step

  1. Distribute x: x(x^2 + 2x + 1) = x^3 + 2x^2 + x
  2. Distribute −3: −3(x^2 + 2x + 1) = −3x^2 − 6x − 3
  3. Add results: x^3 − x^2 − 5x − 3

Answer: x^3 − x^2 − 5x − 3

Tip: A 3-term polynomial times a 2-term polynomial creates 6 products before combining.

Example 3 — Difference of Squares

Multiply (3x − 1)(3x + 1).

Step-by-step

  1. Distribute: 3x(3x + 1) − 1(3x + 1)
  2. Multiply: = (9x^2 + 3x) + (−3x − 1)
  3. Combine like terms: 9x^2 − 1

Answer: 9x^2 − 1

Tip: This follows (a − b)(a + b) = a^2 − b^2.

Frequently Asked Questions

Q: Do I need to type parentheses?

No. Parentheses are optional and ignored. Just enter each polynomial expression.

Q: What inputs are supported?

Single-variable polynomials with +/− signs, integer/decimal coefficients, and exponents using ^.

Q: Can I type something like x(x+2) in one box?

Not in this version. Enter each polynomial as a sum of terms in its own box (example: type x and x+2 separately).

Q: Why am I getting a “Could not parse part” warning?

It usually means an unsupported format (like x2 instead of x^2, or extra symbols). Rewrite using ^ for powers and normal +/− signs.