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Algebra Calculator with steps

Pick Simplify, Expand, Factor or Solve, type the expression and get a result that has been tested against what you entered.

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Answer

Enter your numbers or pick an example — the answer and the steps appear here instantly.

Four actions, one input box

  • Simplify

    Like terms are combined and common factors cancel. If a cancelled factor could make a denominator zero, the outline notes that the value stays excluded.

  • Expand

    Brackets are multiplied out and the terms sorted by power, so (x + 3)(x − 2) becomes x² + x − 6.

  • Factor

    Common factors come out first, then rational roots split the rest: x² − 5x + 6 = (x − 2)(x − 3), 6x² + x − 2 = (2x − 1)(3x + 2) and 2x³ − 8x = 2x(x − 2)(x + 2).

  • Solve

    Equations go to the same engine as our solve-for-x calculator, which returns exact roots and substitutes each one back.

Results that match your input

  • Cross-checked before display

    Each result is evaluated numerically against your original expression with two independent math libraries. A result that fails the comparison is never shown.

  • Honest about irreducible polynomials

    When a polynomial cannot be factored over the rationals, as with x² + 1, you are told so rather than handed a forced answer.

  • More than one variable

    Factoring also works with several letters: x²y − y factors to y(x − 1)(x + 1).

How to use the algebra calculator

  1. Choose the action

    Simplify, Expand, Factor or Solve for the variable. The input box accepts both expressions and equations.

  2. Enter the expression

    Use ^ for powers and brackets for grouping, for example (x + 3)(x - 2), x^3 - 4x or 2x + 5 = 11.

  3. Calculate and read the outline

    The result appears as math with numbered steps showing what was combined, multiplied out or factored. Any decimal that had to be rounded is marked ≈.

  4. Ask for the reasoning

    “Explain step by step” passes the same task to the AI Math Solver for a written walkthrough, and “Ask a follow-up” continues the conversation in AI Chat.

How to factor a polynomial by hand

Start by pulling out the greatest common factor. In 3x³ − 12x every term contains 3x, so 3x³ − 12x = 3x(x² − 4). Then look for special patterns: x² − 4 is a difference of squares, a² − b² = (a − b)(a + b), which leaves 3x(x − 2)(x + 2).

For a trinomial x² + bx + c, find two numbers that multiply to c and add to b. In x² + 7x + 12 they are 3 and 4, so it factors as (x + 3)(x + 4). When the leading coefficient is not 1, use the ac method: for 2x² + 7x + 3, ac = 6, and 1 and 6 add to 7, so split the middle term into 2x² + x + 6x + 3 and group to get x(2x + 1) + 3(2x + 1) = (2x + 1)(x + 3).

For cubics and beyond, the rational root test lists every possible rational root as ±(factor of the constant)/(factor of the leading coefficient). Each candidate r that makes the polynomial zero gives a factor (x − r), and dividing it out leaves a smaller polynomial to work on. If no candidate is a root, there is no linear factor with rational coefficients; for a quadratic that settles it, so x² + 1 and x² − 2 both stay as they are.

Frequently asked questions

Expand multiplies out every bracket and lists the terms by power. Simplify combines like terms and cancels common factors, which can leave brackets in place when that form is shorter.

It means no factorization exists with rational coefficients. For example, x² + 1 only splits using complex numbers as (x − i)(x + i), which lies outside factoring over the rationals.

It marks a value of x that made a denominator zero in the original expression. (x² − 4)/(x − 2) simplifies to x + 2, but x = 2 was never allowed in the original, so it stays excluded.

Every result is compared numerically with your input at test values, using two separate math libraries, and anything that fails is withheld. That check covers the calculator's result; the optional AI explanation is written separately and can contain mistakes.

No. Simplify, Expand, Factor and Solve are free, need no sign-up and run in your browser. The AI explanation is included in the Pro plans* (*fair use: up to 300 runs a day across the writing, study and code tools) or uses 2 credits without a plan, with a free preview of its beginning when you are signed out.

It works with typed input only. For a photographed problem, open the AI Math Solver, which accepts images. Whichever you use, treat worked solutions as study material and stick to your course's rules on AI help.

More algebra help

Turn messy algebra into a clean result

Simplify, expand, factor or solve, with each result verified against your input.

Try the algebra calculator
  • Factoring over the rationals
  • Excluded values noted
  • Numerically verified output