What mathematical operation involves the extraction of common factors?

The operation that involves the extraction of common factors is factorising. This process entails rewriting an expression as a product of its factors, which makes clear what common elements can be factored out. For example, in an expression like 6x + 9, factorising would involve recognizing that both terms share a common factor of 3; thus, it can be rewritten as 3(2x + 3).

This demonstrates how factorising highlights and utilizes the shared factors in mathematical expressions, making it essential in simplifying equations and solving problems. In contexts such as algebra, factorising allows for easier manipulation of expressions, hence its significance in both theoretical and practical applications in engineering and mathematics.