🧮 Algebra Calculator: Simplify, Expand & Factor

Expand brackets, collect like terms and factor — the algebra homework helper.

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Formula at a glance

Algebra Calculator: Square of a sum — (a + b)² = a² + 2ab + b². Example: Expand and simplify → Simplified: 2x² + 2x − 6
How the Algebra Calculator works: Square of a sum — (a + b)² = a² + 2ab + b²

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📘 About the Algebra Calculator

Algebra rewrites expressions into simpler or more useful forms. Expanding multiplies out brackets and collects like terms; factoring does the reverse, writing the expression as a product — the key step for solving equations and simplifying fractions.

Type an expression with any letters. The calculator expands it, collects like terms, factors out common factors (like 3xy) and, for one variable, finds linear factors from rational roots (x² − 4 = (x − 2)(x + 2)). It combines fractions over a common denominator, gives the degree and roots, and evaluates at values you give. Type an equation with “=” to solve it.

🧮 Formula

Square of a sum
(a + b)² = a² + 2ab + b²
Difference of squares
a² − b² = (a − b)(a + b)
Cube of a sum
(a + b)³ = a³ + 3a²b + 3ab² + b³

✏️ Worked examples

Expand and simplify

You enter
Expression(x + 3)(x - 2) + x(x + 1)
What to doSimplify (show all forms)
You get
Simplified2x² + 2x − 6
Factored2(x² + x − 3)
Degree2 (quadratic)
Roots (where it equals 0)x = −2.3027756, x = 1.3027756

2x² + 2x − 6.

Factor a cubic

You enter
Expressionx^3 - 6x^2 + 11x - 6
What to doFactor
You get
Factored(x − 1)(x − 2)(x − 3)
Expandedx³ − 6x² + 11x − 6
Degree3 (cubic)
Roots (where it equals 0)x = 1, x = 2, x = 3

(x − 1)(x − 2)(x − 3).

🧭 How to use this calculator

What you enter

  • Expression
  • What to do
  • Evaluate at (optional)

What you get

  • Simplified
  • Factored
  • Degree
  • Roots (where it equals 0)

❓ Frequently asked questions

What does it mean to simplify an expression?

To combine like terms (3x + 2x = 5x), multiply out where helpful and cancel common factors so the expression is as short as possible.

How do you factor x² + 5x + 6?

Find two numbers that multiply to 6 and add to 5 — 2 and 3 — so x² + 5x + 6 = (x + 2)(x + 3).

Can it factor expressions with two variables?

It takes out common factors (6x²y + 9xy² = 3xy(2x + 3y)) and expands any expression; full factoring is for one variable.