Simplified Result
Review the final form, restrictions, steps, and verification.
Step-by-step transformation
Restrictions and status
Verification samples
| Values | Original | Result | Match |
|---|
Complete calculation record
Recent calculations
Formula and algebra rules used
Like terms share identical variables and powers. Their numerical coefficients can be added or subtracted. Different variable structures must remain as separate algebraic terms.
The distributive rule multiplies every grouped term. Factoring reverses that process by extracting common factors. Both transformations preserve equality across every valid variable value.
| Rule | General form | Example |
|---|---|---|
| Combine like terms | ax + bx = (a + b)x | 3x + 5x = 8x |
| Distributive property | a(b + c) = ab + ac | 2(x + 4) = 2x + 8 |
| Difference of squares | a² − b² = (a − b)(a + b) | x² − 9 = (x − 3)(x + 3) |
| Product of powers | xᵐxⁿ = xᵐ⁺ⁿ | x²x³ = x⁵ |
| Quotient of powers | xᵐ/xⁿ = xᵐ⁻ⁿ | x⁵/x² = x³ |
| Zero exponent | x⁰ = 1, x ≠ 0 | 7x⁰ = 7 |
How to use the calculator
Enter one expression or an equation. Select the required simplification mode and target variable. Press simplify to generate results, restrictions, steps, and checks.
Use explicit multiplication symbols for dependable parsing. Review denominator restrictions before using the reduced expression. Export your work after confirming each displayed transformation carefully.
Example calculations
| Input | Simplified form | Main operation | |
|---|---|---|---|
3*x + 5*x - 2 |
8*x - 2 | Combine like terms | |
2*(x + 4) - 3*x |
8 - x | Expand and combine | |
x^2 + 2*x + x^2 - 4 |
2*x^2 + 2*x - 4 | Polynomial simplification | |
(x^2 - 9)/(x - 3) |
x + 3, x ≠ 3 | Cancel common factors | |
2*x + 6 = 4*x - 8 |
2*x - 14 = 0 | Move terms to one side | |
(a*b + a*c)/a |
b + c, a ≠ 0 | Factor cancellation |
Frequently asked questions
What does simplifying an equation mean?
It rewrites each side in an equivalent, cleaner form. It may combine terms, expand brackets, or reduce fractions. Simplifying does not always isolate the requested variable completely.
Can this calculator solve an equation too?
The main purpose is algebraic simplification. A separate solve option can continue for one variable. Always review restrictions before accepting any displayed solution set.
Which variables can I enter?
You may use letters such as x, y, a, and b. Multiple variables are supported in one expression. Clear multiplication signs improve parsing and reduce input mistakes.
How should multiplication be entered?
Use an asterisk between factors, such as 3*x. Parentheses may also indicate grouped multiplication. Explicit operators make complex expressions easier to interpret correctly.
Does it simplify fractions?
Yes, rational expressions can be reduced where valid. Cancelled factors create restrictions on excluded denominator values. Those original restrictions remain important after simplification is complete.
Can it factor or expand expressions?
Choose the required operation from the calculation mode. Factoring reveals products, while expansion removes grouped products. Both forms remain algebraically equivalent within their valid domains.
How is equivalence checked?
The calculator compares symbolic forms whenever possible. It also tests several safe numerical substitutions. Restricted or undefined sample values are skipped automatically during verification.
Why is a domain restriction displayed?
A denominator cannot equal zero in the original expression. Cancellation may hide that restriction in the result. The excluded value still remains outside the valid domain.
Can I download my work?
You can copy results or download CSV and PDF files. Calculation history remains inside your current browser. Clearing browser storage may remove saved history entries permanently.