Examples for

Simplification

When a mathematical expression is complicated, it is often useful to transform the expression into a form that is easier to understand. That's where simplification comes in. All sorts of math terms have equivalent forms that are more intelligible. Wolfram|Alpha can be used as a simplification calculator to simplify polynomials, Booleans, numbers, rational functions and many other math objects.

Simplification

Simplify radicals, polynomials or any other math expression.

Simplify an expression:

1/(1+sqrt(2))

Simplify a polynomial expression:

simplify x^5-20x^4+163x^3-676x^2+1424x-1209

Simplify a rational expression:

simplify ((x-1)^2(x-2)^3(x^2-1))/(x^3-x^2-4x+4)

Simplify a trigonometric expression:

simplify cos(arcsin(x)/2)

Expansion

Expand mathematical expressions using FOIL and other methods.

Expand a polynomial:

expand (x^2 + 1)(x^2 - 1)(x+1)^3
expand (x + y + z)^10

Boolean Simplification

Find simplified forms of Boolean statements.

Perform Boolean algebra simplification:

Simplify A And B Or A And Not B
simplify (X || Y) || X && Y || Y

Factorization

Factorize quadratic expressions and higher-degree expressions.

Factor a polynomial:

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48
factor x^12 - y^12

Completing the Square

Simplify a polynomial by completing the square.

Complete a square:

complete the square x^2+10x+28

Algebraic Form Conversion

Convert equations to and from exponential and logarithmic forms.

Convert an equation to exponential form:

express log3(x) = 10 in exp form
what is the exponential form of 4log2(x) = 2

Convert an equation to logarithmic form:

express 2^3 = 8 in log form
what is the log form of e^x = 1?

GO FURTHER

Step-by-Step Solutions for AlgebraAlgebra Web App

RELATED EXAMPLES

  • Arithmetic
  • Calculus & Analysis
  • Geometry
  • Logic & Set Theory
  • Polynomials
  • Rational Functions

    • Partial Fractions

    Transform rational expressions by splitting them apart into partial fractions.

    Compute a partial fraction decomposition:

    partial fractions (x^2-4)/(x^4-x)