About Expand Calculator
Expanding removes brackets by multiplying every term by every other term. This page opens with (x + 2)^3, which expands to x^3 + 6x^2 + 12x + 8. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
A cube of a sum follows the pattern (a + b)^3 = a^3 + 3a^2 b + 3a b^2 + b^3. With a = x and b = 2 that gives x^3 + 6x^2 + 12x + 8. The coefficients 1, 3, 3, 1 come from Pascal's triangle.
Like terms are combined after the products are formed, so the result is a polynomial written from the highest power down. Expanding is the reverse of factoring, and the graph of the input and the result lie on the same curve.
How to use Expand 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.
Worked examples
(x + 2)^3 gives x^3 + 6*x^2 + 12*x + 8
Binomial cube.
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.
What is (x + 2)^3 expanded?
It is x^3 + 6x^2 + 12x + 8. Using (a + b)^3 = a^3 + 3a^2 b + 3a b^2 + b^3 with a = x and b = 2 gives 1x^3 + 3(2)x^2 + 3(4)x + 8.
How do I expand a product of two brackets?
Multiply each term in the first bracket by each term in the second, then collect like terms. For (x + 1)(x + 3) that gives x^2 + 3x + x + 3 = x^2 + 4x + 3.
How can I check an expansion?
Put a number in both forms. At x = 1, (1 + 2)^3 = 27 and 1 + 6 + 12 + 8 = 27. Or switch to Factor and see if you get the original back.
More Algebra Calculator pages
- Algebra CalculatorSimplify, expand, factor or solve an expression, with the working shown and a graph.
- Simplify CalculatorCombine like terms, tidy powers and cancel common factors, with every move 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.