About Algebra Calculator
This algebra calculator is free, needs no sign-up and runs in your browser, so the expressions you type are never uploaded. Choose what you want to do, type the expression, and read the result with the steps that led to it.
It has four modes. Simplify combines like terms and cancels common factors, Expand multiplies out brackets and powers, Factor writes a polynomial as a product, and Solve finds the roots of an equation in x.
A graph shows the input and the result together, so you can see that a simplified or factored form is the same function, and for an equation it marks the solutions where the curve crosses zero.
How to use Algebra Calculator
- Pick a mode: Simplify, Expand, Factor or Solve.
- Type the expression in the box, for example (x+2)^3, or use the key pad. For Solve, include an equals sign.
- Read the result card for the answer in proper notation.
- Open the steps to see each move, such as expanding, combining terms or cancelling a factor.
- Look at the graph to confirm the result: the input and the answer lie on the same curve, and roots sit on the x axis.
- Copy the answer with the copy button, or switch modes to carry the same expression into another operation.
Features
- Simplify: combines like terms and powers and cancels common factors in fractions.
- Expand: multiplies out products and powers of sums.
- Factor: writes a polynomial in one variable as a product of simpler factors.
- Solve: finds the real and complex roots of a polynomial equation in x.
- Step-by-step working for every mode.
- A graph of the input and the result, with solutions marked on the axis.
- A live preview and a math key pad, so input is easy on a phone.
- Clear errors for input that cannot be read.
Identities used by the calculator
Most of the work uses a few standard identities. The difference of squares and the perfect square formulas drive factoring and expanding, and the quadratic formula gives the roots of a second-degree equation.
a^2 - b^2 = (a - b)(a + b)
(a + b)^2 = a^2 + 2ab + b^2
(a + b)^3 = a^3 + 3a^2*b + 3a*b^2 + b^3
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)Worked examples
Simplify (x^2-1)/(x-1) gives x + 1
Factor the top and cancel x - 1.
Expand (x+2)^3 gives x^3 + 6*x^2 + 12*x + 8
Cube of a sum.
Factor x^3-x^2-4x+4 gives (x - 1)*(x - 2)*(x + 2)
Roots at 1, 2 and -2.
Solve x^2-5x+6=0 gives x = 2, x = 3
Factors as (x - 2)(x - 3).
Good to know
What the calculator can and cannot do
Factoring and solving work on polynomials in one variable. Simplify and expand accept expressions with more than one letter, but the graph is drawn only for expressions in x.
Results are given in a standard form. The same expression can be written in several equal ways, so a textbook answer may look different. Plug in a number or compare the graphs to check that two forms agree.
A simplified fraction is only equal to the original where the original is defined. For (x^2-1)/(x-1) the result x + 1 holds for every x except 1.
Privacy: how it works
- The algebra is done by code running in your browser tab. Your expressions are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Use * for products when you can: 4*x is unambiguous.
- Check a factored form by switching to Expand and typing it in. You should get the original polynomial.
- To solve a quadratic, put every term on one side so the equation ends in = 0, or let the calculator move the terms.
- Powers use ^, so x squared is x^2 and the square root of x is sqrt(x).
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your expressions are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your expressions are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I simplify an algebraic expression?
Combine like terms, apply the laws of powers, and cancel factors that appear on the top and bottom of a fraction. Choose Simplify and the calculator shows each of those moves.
What is the difference between expanding and factoring?
They are opposites. Expanding multiplies brackets out into a sum of terms, for example (x + 2)^3 becomes x^3 + 6x^2 + 12x + 8. Factoring turns a sum back into a product.
How do I factor a polynomial?
Look for a common factor, a known pattern such as a difference of squares, or a root that makes the polynomial zero. The calculator finds the roots and writes the matching factors.
How do I solve an equation for x?
Choose Solve and type the equation with an equals sign. For a polynomial the calculator factors or uses the quadratic formula and lists every root, including complex ones.
Does it show complex solutions?
Yes. If an equation has no real solution, such as x^2 + 1 = 0, the roots are shown with the imaginary unit i.
Why does the graph not appear for my expression?
The graph needs an expression in x alone. If you use another letter, the working and the answer are still shown but nothing is drawn.
Can I solve a system of equations here?
Not in this tool. Use the equation solver, which handles systems of two and three linear equations.
Popular Algebra Calculator pages
- Simplify CalculatorCombine like terms, tidy powers and cancel common factors, with every move shown.
- Expand CalculatorMultiply out brackets and powers of sums into a polynomial, with the working shown.
- Factor CalculatorWrite a polynomial as a product of simpler factors, with the working shown.
- Solve for X CalculatorType an equation in x and get every solution, with the working and a graph.