simplifying

Simplifying is the process of reducing a mathematical expression or problem to a form that is easier to work with while preserving its value or meaning. The goal is to remove redundancy, combine like terms, and present the result in a standard, irreducible form.

In arithmetic and algebra, common tasks include reducing fractions by dividing numerator and denominator by their greatest common divisor, and simplifying expressions by combining like terms and applying the distributive, associative, and commutative laws. Factoring out common factors can reveal cancellations in fractions or help solve equations. For example, 6/8 simplifies to 3/4, and x^2 + 2x simplifies to x(x + 2). In radical expressions, simplification usually means factoring inside the radical to pull out square factors, as in sqrt(50) = 5 sqrt(2). Rational expressions are simplified by factoring the numerator and denominator and canceling common factors when allowed.

Beyond algebra, simplification also means rewriting a problem or statement to expose essential structure, making calculations or reasoning easier and reducing potential error.

Notes: There is often no single universally accepted “simplest form”; conventions depend on context. Computer algebra systems implement rules-based rewriting to a chosen canonical form, which may vary with the system and settings.