All calculatorsSimplify Expression Calculator
Simplify algebraic expressions fast: combine like terms, expand, reduce fractions, and factor out a GCF. Includes quick picks, step-by-step, and domain warnings when canceling terms.
Background
“Simplify” means rewrite an expression into a cleaner form without changing its value. Some moves (like canceling (x−1)) are only valid when that factor isn’t zero — so we’ll show the restriction (like x ≠ 1) when needed.
How to use this calculator
- Choose a mode: Simplify, Expand, Factor GCF, or Reduce fraction.
- Type your expression using ^ for exponents.
- Click Calculate (or tap a quick pick).
- Turn on Step-by-step to see exactly what changed.
Safety note: If we cancel a factor like (x−1), we’ll show the restriction (like x ≠ 1).
How this calculator works
- Combine like terms: add/subtract terms with the same variable part (e.g., 3x + 2x = 5x).
- Expand: distribute multiplication over addition (FOIL is a special case), e.g. (x+2)(x−5) = x² − 3x − 10.
- Factor GCF: pull out the greatest common factor, e.g. 6x²y + 9xy² = 3xy(2x + 3y).
- Reduce fractions: cancel common factors in numerator/denominator (with domain restrictions), e.g. (x²−1)/(x−1) = (x+1) but only when x ≠ 1.
Important: canceling factors can remove “holes” in the domain. That’s why we show restrictions when simplification uses cancellation.
Formula & Equation Used
Distributive property: a(b + c) = ab + ac
Combining like terms: ax + bx = (a+b)x
Difference of squares (common factorization): x² − 1 = (x−1)(x+1)
Safe cancellation rule: (A·B)/(A·C) = B/C only if A ≠ 0
Example Problem & Step-by-Step Solution
Example 1 — simplify by combining like terms
Simplify: 3(x+2) − x
- Distribute: 3(x+2) = 3x + 6
- Subtract x: 3x + 6 − x = 2x + 6
- Final: 2x + 6
Example 2 — reduce a rational expression (with restriction)
Reduce: (x² − 1)/(x − 1)
- Factor the numerator: x² − 1 = (x−1)(x+1)
- Cancel the common factor: (x−1)
- Simplified result: x + 1
- Restriction: since we canceled (x−1), we must have x ≠ 1
Example 3 — factor out the GCF
Factor: 6x²y + 9xy²
- Numeric GCF of 6 and 9 is 3
- Common variables: both terms include x and y
- Factor: 6x²y + 9xy² = 3xy(2x + 3y)
Frequently Asked Questions
Q: What kinds of expressions can I simplify here?
This calculator is built for algebraic expressions using + − × ÷, parentheses, and exponents like x^2. It works great for polynomials and many rational expressions.
Q: Why do you show “restrictions” like x ≠ 1?
Canceling a factor like (x−1) is only valid when that factor isn’t zero. The restriction keeps the simplified form mathematically correct.
Q: What’s the difference between Simplify and Expand?
Expand distributes multiplication (often creating a longer expression), while Simplify combines and reduces to a cleaner form.
Q: Will it simplify trig/log expressions too?
Not in this version. This tool focuses on core algebra. (Trig/log rules can be added in a future version.)
