Expression Simplifier
How to simplify algebraic expressions
Type a polynomial in x (like 3x^2 + 2x − 5) and press Simplify. Like terms are combined step by step: coefficients of x² together, coefficients of x together, constants together.
What are like terms?
Like terms have the same variable raised to the same power: 3x² and 5x² are like terms, but 3x² and 3x are not. Only like terms can be combined by adding their coefficients.
Worked example
Simplify 3x² + 2x − 5 + x² − x: group x² terms (3x² + x² = 4x²), x terms (2x − x = x), constants (−5). Result: 4x² + x − 5.
Frequently asked questions
Add the coefficients of terms with identical variable parts. 2x + 5x = 7x because both are “x” terms.
Not yet. This simplifier combines like terms in sums. Use the factoring calculator to work with products.
If coefficients cancel (x − x = 0), the term vanishes. That is correct: the terms genuinely cancel out.
The grouping rule behind simplifying
Simplifying a polynomial is bookkeeping, not new maths. You sort every term by its variable part, add the numbers in front of matching terms, and leave unlike terms untouched. Writing the groups out in a fixed order, highest power first, makes slips much easier to spot.
Watch the signs as you group. A minus sign belongs to the term that follows it, so -4x and +9x combine to +5x, not to +13x or -13x.
Example: Simplify 6x^2 – 4x + 3 + 2x^2 + 9x – 8
Step 1, Group the x^2 terms: 6x^2 + 2x^2 = 8x^2, because 6 + 2 = 8.
Step 2, Group the x terms: -4x + 9x = 5x, because -4 + 9 = 5.
Step 3, Group the constants: 3 – 8 = -5.
Step 4, Write the result in order: 8x^2 + 5x – 5. A spot check at x = 2 gives 37 from both the original expression and the simplified one, so they match.
Common mistakes
- Combining unlike terms: Adding 3x^2 and 3x into a single term is not allowed, because the powers differ.
- Losing a sign: In 5x – 3x the second term is negative, so the result is 2x. Copy each sign with its term when you regroup.
- Changing a power: Adding coefficients never changes the exponent. 4x^2 + x^2 is 5x^2, not 5x^4.
When to use this calculator
Use it before solving, graphing, or substituting a value into a long expression, and whenever two formulas have been added together on paper. A shorter expression is quicker to work with and far easier to check. The tool is free to use for quick homework checks as well.
More questions
The value is the same in any order, but the usual convention is descending powers: x^2 terms first, then x terms, then constants. Writing 8x^2 + 5x – 5 is clearer than -5 + 5x + 8x^2.
It is usually left unwritten. A term shown simply as x means 1x, and x^2 means 1x^2. The 1 is still there in the maths, it is just hidden by convention to keep expressions tidy.
Pick a simple value such as x = 2, work out the original expression and your simplified version, and compare. If both give the same number, the two forms are very likely equivalent.