Simplify Expression Calculator
Simplify algebraic expressions fast: combine like terms, expand, factor (GCF and integer-root linear factors), and reduce fractions. Includes quick picks, step-by-step, and domain warnings when canceling terms or using negative exponents.
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, or Reduce fraction.
- Type your expression using ^ for exponents (negative exponents like x^-2 work too).
- 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), or convert a negative exponent, we’ll show the restriction (like x ≠ 1).
Supported / not supported yet
Supported well
- Combining like terms and simplifying polynomials
- Expanding products such as (x+2)(x−5), with FOIL-style step breakdowns
- Factoring out a GCF, and splitting into linear factors when there are integer roots — e.g. x² − 4 → (x − 2)(x + 2) or x² + 2x + 1 → (x + 1)²
- Reducing common rational-expression patterns, including difference of squares and simple trinomial factors
- Negative integer exponents, like x^-2 = 1/x²
Not supported yet
- Trig, logarithmic, radical, absolute-value, or complex-number simplification
- Advanced CAS-style transformations
- Non-integer or variable exponents
- Factoring polynomials whose roots aren't integers (e.g. x² + x + 1 stays unfactored)
- Very complex multivariable factoring beyond GCF-style simplification
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: pull out the GCF, then repeatedly strip out any integer-root linear factors (grouping repeats into a power), e.g. 6x²y + 9xy² = 3xy(2x + 3y) or x² − 4 = (x − 2)(x + 2).
- 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 — and the same applies when a negative exponent gets rewritten as a fraction, since the base still can’t be zero.
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)
Negative exponent: a^(−n) = 1/aⁿ when a ≠ 0
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 into linear factors
Factor: x² − 4
- No numeric or monomial GCF to pull out (coefficients are 1 and −4).
- Check for integer roots: x = 2 and x = −2 both make the expression 0.
- Factor: x² − 4 = (x − 2)(x + 2)
Example 4 — 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 or 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. The same idea applies when a negative exponent is rewritten as a fraction — the base still can’t be zero.
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: How far can Factor mode actually factor something?
It pulls out the GCF, then looks for integer roots (whole-number values that make the expression 0) and splits those off as linear factors — repeating for repeated roots, like x² + 2x + 1 → (x + 1)². If a polynomial has no integer roots (like x² + x + 1), it's left as-is rather than guessed at.
Q: Will it simplify trig/log expressions too?
Not in this version. This tool focuses on core algebra: polynomials, many rational expressions, expansion, factoring, and common factor cancellation. Trig/log/radical simplification requires a more advanced CAS engine.
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