Simplify algebraic expressions without changing their value
This simplifying expressions calculator expands brackets, distributes negative signs and combines like terms in a supported polynomial expression. You can use x, y and z, whole-number powers, ordinary decimal coefficients and fractions formed by dividing by constants. The result is an expanded expression with exact reduced fractional coefficients.
Simplifying an expression is different from solving an equation. The input 3(x + 2) − 2x + 4 has no equals sign and simplifies to x + 10. It does not ask for a single value of x. For an equation with one linear unknown, use the Linear Equation Calculator. To find supported polynomial factors instead of expanding brackets, use the Polynomial Factoring Calculator.
How to use the simplifying expressions calculator
- Type one supported expression, using lowercase x, y or z. Enter 3(x + 2) − 2x + 4 to reproduce the first example.
- Use parentheses for grouping and ^ for powers. Multiplication may be explicit, such as 2*x, or implicit before a variable or opening bracket, such as 2x and (x + 1)(x − 1).
- Select Calculate. Read the expanded answer, coefficient arithmetic and the operation-specific steps.
- Check the stated limits if an input is rejected. The calculator does not silently treat a function or variable denominator as a polynomial.
Editing the expression clears the old result so that it cannot be confused with a new input. Reset empties the form. Copy, Download and Print keep the result with its calculation steps. Expressions are processed in the browser; no calculation server is needed.
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For an optional numerical check, browse scientific calculators (paid link). Confirm the supported functions; a numerical device does not necessarily reproduce this tool’s symbolic working. No purchase is needed.
Distributive property and combining like terms
Multiplication distributes over every term in a sum. For example, 3(x + 2) becomes 3x + 6. Subtraction applies to the entire expression that follows it: −(2x − 5) becomes −2x + 5. The working records these operations as the expression is processed.
Like terms must have exactly the same variable powers. The terms 3xy and −2xy combine to xy, but x and x² remain separate. Multiplying x² by x adds the exponents and gives x³. The displayed order is decreasing total degree, with ties ordered by powers of x, then y, then z.
Accepted decimal coefficients are converted to fractions before arithmetic. Thus 0.1x + 0.2x is exactly (3/10)x rather than a binary floating-point approximation. This is separate from the Scientific Calculator, which evaluates numerical expressions rather than returning a symbolic polynomial.
Worked examples: expand brackets and collect like terms
For 3(x + 2) − 2x + 4, distribute 3 to obtain 3x + 6 − 2x + 4. Combine 3x − 2x to get x, then combine 6 + 4 to get 10. The simplified expression is x + 10, and it has the same value as the original for every real x.
For (x + 3)(x − 3), multiply each term in the first bracket by each term in the second: x² − 3x + 3x − 9. The two middle terms cancel, leaving x² − 9. This expansion is the reverse of recognizing a difference-of-squares factorization.
For (2x + 1)/3 + x/6, divide the coefficients by their constant denominators and use a common denominator. The x coefficient is 2/3 + 1/6 = 5/6, so the result is (5/6)x + 1/3. The Fraction Calculator can check that coefficient addition separately.
For 2xy + 3yx − y², multiplication of variables is commutative, so xy and yx describe the same powers. The result is 5xy − y². In contrast, 2x + 3y cannot be combined into 5xy.
Reading the result and checking your work
The term count includes only nonzero terms in the expanded output. Total degree is the largest sum of variable exponents in any term: x²y has total degree three. A nonzero constant has degree zero, while the zero polynomial has no defined degree in the convention used here.
The final step also evaluates the expanded expression at x = 2, y = −1 and z = 3 as a numerical reference. One substitution is not proof that two expressions are identical; the expansion and exact coefficient operations are the algebraic method. For a separate check, substitute the same values into the original expression and compare with that reference.
Unary minus is applied after a power, so −x² means −(x²), while (−x)² is positive x². Multiplication and division are processed left to right. Avoid ambiguous shorthand such as x/2x: write (x/2)*x or x/(2x) to state your intended grouping. The second form is outside this tool’s variable-denominator scope.
Supported expressions and limits
This version supports polynomial expressions in x, y and z with +, −, multiplication, parentheses, whole-number powers from zero through ten and division by nonzero constant expressions. The expansion must have total degree at most ten and at most 60 nonzero terms. Input length is limited to 240 characters, 160 tokens and 80 recorded operation stages. Deeply nested or extremely large exact intermediate values are rejected.
Each numeric literal must be an ordinary number of magnitude at most 1,000,000 with no more than six decimal places. Scientific notation, commas, equations, functions, radicals, negative powers and variable denominators are not supported. Use a slash to form a fractional coefficient, such as (1/3)x. A zero denominator is rejected, and literal 0^0 is not supported.
The calculator expands and collects terms; it does not perform general rational-function cancellation, factorization, equation solving or trigonometric identities. Choosing the right task matters: a correct expanded polynomial is not automatically a solution set or a factored form. Unsupported inputs receive an explanation instead of a guessed answer.
Simplifying Expressions Calculator FAQs
Sources and methodology
These educational references explain the underlying mathematics. This independently implemented tool is not affiliated with their publisher. Supported methods, numerical precision and restrictions are described above.