Master algebraic concepts with our powerful calculator suite. Solve equations, work with polynomials, simplify expressions, analyze functions, and more with step-by-step solutions.
Our advanced equation solver handles linear, quadratic, polynomial, and systems of equations with step-by-step solutions. Enter your equation below to get started.
Solve polynomial equations of any degree. Get exact and numerical solutions with detailed steps.
Form: ax + b = 0
Example: 2x + 3 = 7
Solution: x = 2
Form: ax² + bx + c = 0
Example: x² + 4x + 4 = 0
Solution: x = -2 (double root)
Form: anx^n + ... + a1x + a0 = 0
Example: x³ - 6x² + 11x - 6 = 0
Solution: x = 1, 2, 3
Solve systems of linear equations with multiple variables. Get step-by-step solutions using elimination, substitution, or matrix methods.
1. Solve one equation for one variable
2. Substitute that expression into the other equation
3. Solve for the remaining variable
4. Substitute back to find the other variable
1. Multiply equations to make coefficients of one variable equal
2. Add or subtract equations to eliminate that variable
3. Solve for the remaining variable
4. Substitute back to find the other variable
1. Write the system in matrix form Ax = b
2. Find the inverse of A
3. Multiply both sides by A⁻¹
4. Solution is x = A⁻¹b
Solve equations with parameters or find values of parameters for specific solutions.
Visualize equations and their solutions with our interactive graphing tool.
Perform operations on polynomials including factoring, expanding, finding roots, and analyzing properties. Our tools handle polynomials of any degree with multiple variables.
Factor polynomials into their irreducible components.
Example: 3x² + 6x = 3x(x + 2)
a² - b² = (a + b)(a - b)
Example: x² - 9 = (x + 3)(x - 3)
a² + 2ab + b² = (a + b)²
a² - 2ab + b² = (a - b)²
Example: x² + 6x + 9 = (x + 3)²
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
Example: x³ - 8 = (x - 2)(x² + 2x + 4)
Expand and simplify polynomial expressions.
(a + b)(c + d) = ac + ad + bc + bd
Example: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
Example: (x + 1)² = x² + 2x + 1
(a + b)ⁿ = Σ(k=0 to n) (n choose k) aⁿ⁻ᵏbᵏ
Example: (x + y)³ = x³ + 3x²y + 3xy² + y³
Analyze properties of polynomials including degree, roots, coefficients, and more.
The highest power of the variable in the polynomial.
Example: x³ + 2x² + x + 3 has degree 3
The coefficient of the term with the highest degree.
Example: In 2x³ + x² + 4, the leading coefficient is 2
Values of x for which P(x) = 0.
Example: x² - 4 has roots at x = 2 and x = -2
Visualize polynomial functions and analyze their graphs.
Simplify algebraic expressions, rationalize denominators, combine like terms, and more. Our tools handle complex expressions with multiple variables and operations.
Simplify algebraic expressions by combining like terms and applying algebraic properties.
Group and add/subtract terms with the same variables and exponents.
Example: 3x + 2y - 5x + 4y = (3 - 5)x + (2 + 4)y = -2x + 6y
a(b + c) = ab + ac
Example: 2(x + 3y) = 2x + 6y
x^a · x^b = x^(a+b)
x^a ÷ x^b = x^(a-b)
(x^a)^b = x^(a·b)
Example: x^2 · x^3 = x^5
Simplify complex algebraic expressions including those with square roots, fractions, and trigonometric functions.
sin²(x) + cos²(x) = 1
tan²(x) + 1 = sec²(x)
1 + cot²(x) = csc²(x)
sin(2x) = 2sin(x)cos(x)
cos(2x) = cos²(x) - sin²(x) = 2cos²(x) - 1 = 1 - 2sin²(x)
Analyze and manipulate rational functions, find domains, asymptotes, and more. Our tools provide comprehensive analysis of rational expressions.
Simplify, add, subtract, multiply, and divide rational expressions.
Factor numerator and denominator, then cancel common factors.
Example: (x² - 4)/(x - 2) = ((x - 2)(x + 2))/(x - 2) = x + 2 for x ≠ 2
Find a common denominator, then add/subtract numerators.
Example: 1/x + 2/y = (y + 2x)/(xy)
Multiply numerators and denominators, then simplify.
Example: (x/y) · (y/z) = xy/yz = x/z
Decompose rational expressions into simpler fractions.
Analyze rational functions to find domains, vertical and horizontal asymptotes, holes, and more.
Perform operations on matrices including addition, multiplication, finding determinants, inverses, eigenvalues, and more.
Perform basic matrix operations like addition, subtraction, multiplication, and scalar multiplication.
Calculate determinants, inverses, eigenvalues, and more for matrices.
