Ausklammerung

Ausklammerung is a mathematical operation, also known as factoring out or pulling out a common factor. It is the reverse of the distributive property. In essence, it involves identifying a common factor in two or more terms and rewriting the expression by placing that common factor outside a parenthesis, with the remaining parts of the terms inside. For example, if you have the expression ax + ay, the common factor is 'a'. Applying Ausklammerung, you would rewrite this as a(x + y). Similarly, for 2x + 4y, the common factor is 2, and the expression becomes 2(x + 2y). This technique is fundamental in algebraic manipulation, simplifying expressions, solving equations, and factoring polynomials. It allows for a more compact representation of mathematical expressions and is a crucial step in many algebraic procedures. The concept is widely applied in arithmetic as well as higher mathematics.