The process involves finding the greatest common factor (GCF) of the terms 26rs, 52r, and 39rs. The GCF is the largest expression that divides evenly into all given terms. In this case, the coefficients 26, 52, and 39 share a common factor of 13. The variables r and s also appear in each term. The lowest power of r present is r, and the lowest power of s is s. Therefore, the GCF is 13rs. Dividing each term by the GCF yields the factored expression: 13rs(2rs + 4r + 3s).
Factoring expressions plays a crucial role in simplifying algebraic equations and expressions. This simplification allows for easier manipulation and solution of complex mathematical problems. Historically, the development of factoring techniques contributed significantly to advancements in algebra and number theory. It allows mathematicians to break down complex expressions into simpler components, revealing underlying structures and relationships.
