Algebra - Wolfram|Alpha Examples

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Algebra

Algebra is one of the core subjects of mathematics. Algebra consists of the study of variables within number systems, along with operations that act on numbers and symbols. Wolfram|Alpha is a tremendous resource for solving equations; exploring polynomials; and studying fields, groups, vectors and matrices.

Equation Solving ›

Solve equations in one or more variables both symbolically and numerically.

Solve a polynomial equation:

solve x^2 + 4x + 6 = 0

Solve a system of linear equations:

x+y=10, x-y=4

Solve an equation with parameters:

solve a x^2 + b x + c = 0 for xMore examplesRational Functions ›

Compute discontinuities and other properties of rational functions.

Compute properties of a rational function:

(x^2-1)/(x^2+1)

Compute a partial fraction decomposition:

partial fractions (x^2-4)/(x^4-x)More examplesQuaternions ›

Perform computations with the quaternion number system.

Get information about a quaternion:

quaternion: 0+2i-j-3k

Do calculations with quaternions:

quaternion -Sin[Pi]+3i+4j+3k multiplied by -1j+3.9i+4-3kMore examplesDomain & Range ›

Find the domain and range of mathematical functions.

Compute the domain of a function:

domain of f(x) = x/(x^2-1)

Compute the range of a function:

range of e^(-x^2)More examplesPolynomials ›

Solve, plot and find alternate forms of polynomial expressions in one or more variables.

Compute properties of a polynomial in several variables:

x^3 + x^2 y + x y^2 + y^3

Factor a polynomial:

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48More examplesSimplification ›

Simplify algebraic functions and expressions.

Simplify an expression:

1/(1+sqrt(2))simplify x^5-20x^4+163x^3-676x^2+1424x-1209simplify cos(arcsin(x)/2)More examplesFinite Groups ›

Discover properties of groups containing a finite number of elements.

Get information about a finite group:

alternating group A_5

Ask about a property of a group:

order of the monster group

Do algebra with permutations:

perm (1 2 3 4)^3(1 2 3)^-1More examples

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Step-by-Step Solutions for AlgebraAlgebra Web App

RELATED EXAMPLES

Arithmetic

Calculus & Analysis

Geometry

Linear Algebra

RELATED WOLFRAM RESOURCES

Wolfram Calculus & Algebra

Matrices ›

Find properties and perform computations on matrices.

Do basic arithmetic on matrices:

{{0,-1},{1,0}}.{{1,2},{3,4}}+{{2,-1},{-1,2}}

Compute eigenvalues and eigenvectors of a matrix:

eigenvalues {{4,1},{2,-1}}More examplesFinite Fields ›

Discover properties of fields containing a finite number of elements.

Compute properties of a finite field:

Z/7Z

Compute a specific property:

number of primitive polynomials of GF(3125)More examples