Algebra Simplifier
Simplify any algebraic expression instantly — linear, quadratic, polynomial, or rational. Get the fully reduced form with a complete step-by-step breakdown.
Try: 3(x+2) - x , x^2 + 5x + 6 , (x^2-9)/(x-3)
Algebra Expression Types — Examples
| Type | Input Expression | Simplified | Method |
|---|---|---|---|
| Linear | 3x + 2 - x + 5 | 2x + 7 | Combine like terms |
| Quadratic | x^2 + 5x + 6 | (x+2)(x+3) | Factor trinomial |
| Polynomial | 2x^3 - 4x^2 + 2x | 2x(x-1)² | Factor out GCF |
| Rational | (x^2-4)/(x+2) | x - 2 | Cancel factors |
| Exponents | x^3 * x^2 / x^4 | x | Apply power laws |
| Nested | 2(3(x+1) - 2) | 6x + 2 | Expand from inside out |
Algebra Simplification Rules
Distributive Property
a(b + c) = ab + ac
Remove brackets by distributing the factor
Combining Like Terms
ax + bx = (a+b)x
Add/subtract terms with identical variables
Power Rule (Multiply)
xᵃ · xᵇ = xᵃ⁺ᵇ
Combine exponents when multiplying
Power Rule (Divide)
xᵃ / xᵇ = xᵃ⁻ᵇ
Subtract exponents when dividing
Power of a Power
(xᵃ)ᵇ = xᵃᵇ
Multiply exponents when raising to a power
Zero Exponent
x⁰ = 1 (x ≠ 0)
Any nonzero base raised to 0 equals 1
Negative Exponent
x⁻ⁿ = 1/xⁿ
Move negative exponent to denominator
FOIL Method
(a+b)(c+d) = ac+ad+bc+bd
Expand product of two binomials
Frequently Asked Questions
What is an algebra simplifier?
An algebra simplifier is a tool that rewrites algebraic expressions in their most compact, reduced form. It applies algebraic rules such as combining like terms, distributing, factoring, and cancelling common factors to produce an equivalent but simpler expression.
How do I simplify algebra expressions?
To simplify algebra expressions: (1) Remove parentheses using the distributive property, (2) Combine like terms by adding coefficients of identical variable terms, (3) Apply exponent rules to simplify powers, (4) Factor and cancel common terms in fractions, (5) Arrange in standard form from highest to lowest degree.
Can this algebra simplifier handle quadratic expressions?
Yes. The algebra simplifier handles quadratic expressions such as x^2 + 5x + 6, simplifying or factoring them into (x+2)(x+3). It also handles quadratic equations when you set them equal to zero.
What is the difference between simplifying and evaluating algebra?
Simplifying rewrites an expression in a shorter equivalent form without finding a numerical answer. Evaluating substitutes specific values for variables to get a number. For example, simplifying 3x + 2x gives 5x, while evaluating 5x at x=4 gives 20.
Can I simplify rational algebra expressions (fractions)?
Yes. Enter rational expressions like (x^2 - 9)/(x - 3) and the simplifier factors and cancels to give x + 3. Make sure to note any excluded values where the denominator equals zero.