Algebra Simplifier with Steps
Expand brackets, factorise, simplify fractions and split into partial fractions. Calvo works with exact fractions, shows each step, and checks the answer by multiplying it back out.
Use * for multiplication (2x and (x+1)(x-1) also work), ^ for powers, and / for fractions. Several letters are fine for Expand, Factor and Simplify.
What each mode does
| Mode | Example | Result |
|---|---|---|
| Expand | (x + 2)(x − 3) | x² − x − 6 |
| Factor | x² − 5x + 6 | (x − 2)(x − 3) |
| Simplify | (x² − 4)/(x − 2) | x + 2 |
| Partial fractions | (3x + 5)/(x² + x − 2) | 8/(3(x − 1)) + 1/(3(x + 2)) |
Worked example: partial fractions
Split (3x + 5)/((x − 1)(x + 2)). Write A/(x − 1) + B/(x + 2). Multiply out: 3x + 5 = A(x + 2) + B(x − 1). Matching coefficients gives A + B = 3 and 2A − B = 5, so A = 8/3 and B = 1/3.
How Calvo checks the answer
Every factorisation is multiplied back out with exact fractions and must equal the original. Expand, Simplify and Partial fractions answers are also compared with the original expression at several test values.
What is not supported
Only polynomials and fractions of polynomials: no sin, ln, ex or square roots. Factoring is over the rational numbers, so x² − 2 is left as it is. Partial fractions needs one letter and a denominator whose factors are linear or quadratic.
FAQ
How do I factor a quadratic step by step?
Take out any common factor, then look for two numbers that multiply to ac and add to b, or use the rational root test. Calvo shows the root it finds and the division that follows.
How do I expand (x+2)^3?
Use the binomial theorem: x^3 + 3x^2(2) + 3x(2^2) + 2^3 = x^3 + 6x^2 + 12x + 8.
How do I simplify an algebraic fraction?
Factor the top and the bottom, cancel the common factors, and remember the cancelled factor cannot be zero in the original expression.
What are partial fractions?
A way to split one fraction into simpler ones, such as 1/(x^2-1) = 1/(2(x-1)) - 1/(2(x+1)). It is used for integration and in solving equations.
Does it factor expressions with two letters?
Yes. It handles common factors, differences of squares and cubes, perfect squares and factoring by grouping, for example xy + 2x + 3y + 6 = (x + 3)(y + 2).