Algebra Calculators
Explore free algebra calculators for solving equations, factoring polynomials, finding quadratic roots, working with inequalities, and analyzing functions.
Available Algebra Solvers
Select a calculator to view formula and step-by-step solution
Basic Algebra
4 calculators
Simplify Algebraic Expressions
Simplify complex algebraic expressions by combining like terms and applying order of operations.
Evaluate Expression Calculator
Evaluate algebraic expressions by substituting specific numerical variable values.
Combine Like Terms Calculator
Group and combine identical variable terms and constants easily.
Expand Algebraic Expressions (FOIL)
Expand parentheses and multiply algebraic terms using distributive property.
Linear Equations
6 calculators
Linear Equation Solver (ax + b = c)
Solve standard single-variable linear equations with full step-by-step balance solution.
One-Step Equation Calculator
Solve fundamental one-operation algebraic equations (addition, subtraction, multiplication, division).
Two-Step Equation Calculator
Solve two-operation linear equations with variable isolation method.
Multi-Step Equation Calculator
Solve multi-step equations with variables on both sides and parentheses.
Equation with Fractions Calculator
Solve linear equations containing rational fractions using LCD method.
Equation with Decimals Calculator
Solve linear equations containing decimal coefficients and constants.
Linear Inequalities
3 calculators
Linear Inequality Solver
Solve single-variable linear inequalities with 1D number line graphs and interval notation.
Compound Inequality Calculator
Solve 3-part bounded inequalities with connecting interval line segments.
Absolute Value Inequality Calculator
Solve absolute value inequalities (|ax + b| < c and |ax + b| > c).
Systems of Equations
4 calculators
2Γ2 System of Equations Calculator
Solve simultaneous 2-variable linear equations using Cramer rule and intersecting line graphs.
3Γ3 System of Equations Calculator
Solve 3-variable linear systems (x, y, z) using Gaussian elimination.
Substitution Method Calculator
Solve simultaneous linear systems step-by-step using algebraic substitution.
Elimination Method Calculator
Solve systems of equations step-by-step using linear elimination.
Polynomials
6 calculators
Polynomial Calculator
Master polynomial solver for standard algebraic operations and form analysis.
Polynomial Addition Calculator
Add two or more algebraic polynomials by combining like terms.
Polynomial Subtraction Calculator
Subtract algebraic polynomials with sign distribution.
Polynomial Multiplication (FOIL)
Multiply binomials, trinomials, and polynomials using grid and FOIL methods.
Polynomial Division Calculator
Perform algebraic polynomial long division and synthetic division.
Polynomial Factoring Calculator
Factor higher-degree polynomials into linear and quadratic factors.
Quadratic Equations
4 calculators
Quadratic Formula Solver
Solve second-degree equations axΒ² + bx + c = 0 with interactive parabola graphs.
Quadratic Factoring Calculator
Factor quadratic trinomials axΒ² + bx + c into two binomials (px + q)(rx + s).
Discriminant Calculator (Ξ = bΒ² - 4ac)
Calculate the discriminant and determine the nature of quadratic roots.
Completing the Square Calculator
Transform quadratic polynomials into a perfect square binomial (x + p)Β² = q.
Exponents & Radicals
5 calculators
Exponent Calculator (aα΅)
Calculate powers, base numbers, and laws of exponents.
Negative Exponent Calculator
Convert and simplify negative powers into fractions (xβ»α΅ = 1/xα΅).
Fractional Exponent Calculator
Convert rational powers into radical expressions (xα΅/α΅ = α΅βxα΅).
Square Root Calculator (βx)
Calculate exact and decimal square roots of positive numbers.
Simplify Radicals Calculator
Simplify square roots into simplest radical form (aβb).
Algebraic Fractions
2 calculators
Simplify Algebraic Fractions
Reduce rational fractions with variables and polynomial terms to lowest terms.
Rational Expression Calculator
Add, subtract, multiply, and divide rational algebraic expressions.
Functions
4 calculators
Function Evaluation Calculator
Evaluate mathematical functions f(x) for given numerical input values.
Domain and Range Calculator
Find the domain and range of functions with real-time curve plotting.
Inverse Function Calculator
Find the algebraic inverse function fβ»ΒΉ(x) step-by-step.
Composite Function Calculator
Calculate composition of two functions (f(g(x)) and g(f(x))).
Advanced Alzebra
6 calculators
Absolute Value Equation Calculator
Solve linear absolute value equations (|ax + b| = c) with two-branch solutions.
Cubic Equation Calculator
Find real and complex roots for 3rd-degree cubic polynomial equations.
Complex Number Calculator
Add, subtract, multiply, and divide complex numbers (a + bi).
Partial Fraction Decomposition
Decompose rational fractions into simpler partial fractions for calculus.
Direct and Inverse Variation Calculator
Solve direct variation (y = kx) and inverse variation (y = k/x) equations.
Diamond Problem Calculator
Solve diamond math puzzles by finding two numbers from their product and sum.
Mastering Algebra: The Language of Mathematics
Algebra is one of the foundational pillars of mathematics, bridging basic arithmetic to advanced calculus, physics, engineering, and computer science. Unlike simple arithmetic, which works only with known fixed numbers, algebra introduces variables (such as $x, y, z$) to represent unknown quantities, relationships, and mathematical patterns.
Explore Algebra by Mathematical Domains
Linear Equations & Inequalities
Solve single and multi-step equations ($ax + b = c$), fractions, decimals, and bounded inequalities with coordinate number line graphs.
Quadratic Equations & Parabolas
Find real and complex roots using the Quadratic Formula, calculate the Discriminant ($\Delta = b^2 - 4ac$), and plot interactive parabola curves.
Systems of Linear Equations
Solve simultaneous $2 \times 2$ and $3 \times 3$ linear systems using Substitution, Elimination, and Cramerβs Rule with line intersection graphs.
Polynomials & Factoring
Perform polynomial addition, subtraction, long division, synthetic division, and FOIL binomial expansion step-by-step.
Essential Algebraic Formulas Quick Reference
Below is a summary of the standard formulas utilized throughout our algebra calculation suite:
| Mathematical Topic | Standard Formula | Primary Application |
|---|---|---|
| Linear Form | ax + b = c => x = (c - b)/a | 1st-Degree Variables |
| Quadratic Formula | x = (-b Β± β(bΒ² - 4ac)) / 2a | 2nd-Degree Polynomials |
| Discriminant | Ξ = bΒ² - 4ac | Nature of Roots |
| FOIL Product | (ax+b)(cx+d) = acxΒ² + (ad+bc)x + bd | Binomial Multiplication |
| Difference of Squares | aΒ² - bΒ² = (a - b)(a + b) | Polynomial Factoring |
| Inverse Linear | fβ»ΒΉ(x) = (x - b) / a | Function Inverses |
Why Does Algebra Matter in the Real World?
While algebra is heavily taught for middle school, high school, and college curricula, its practical utility extends directly into every technological industry:
- Software Engineering & Game Development: 3D graphics rendering, collision physics, and artificial intelligence algorithms rely heavily on linear algebra and quadratic vector formulas.
- Financial Modeling & Investment: Compound interest calculations, break-even analysis, profit margins, and risk optimization models are formulated as algebraic functions.
- Architecture & Engineering: Structural load distribution, bridge parabolic arches, and electrical circuit voltages require simultaneous systems of equations.