What process involves rewriting an expression as a product of its factors?

Factorising is the process that involves rewriting an expression as a product of its factors. This technique is fundamental in algebra and is particularly useful for solving equations, simplifying expressions, and analyzing the properties of functions.

When you factor an expression, you identify the numbers or expressions that can be multiplied together to produce the original expression. For instance, in the case of a quadratic expression like (x^2 - 5x + 6), it can be factorised into ((x - 2)(x - 3)). This transformation reveals the roots of the equation more clearly and facilitates further mathematical processes, such as graphing or applying the zero-product property.

The other processes mentioned do not involve rewriting expressions in this particular way. Expanding refers to distributing terms to remove parentheses, which often makes expressions longer rather than shorter or more factored. Simplifying generally means to reduce an expression to its most basic form, which could involve combining like terms but is not specifically about expressing an equation as a product of factors. Differentiating is a calculus operation that finds the rate at which a function is changing, unrelated to factorising. Therefore, the definition and applications of factorising distinctly align with the question asked.