In mathematics, "factor out" refers to the process of taking out common factors from an expression. Synonyms for this term include "factorize," "distribute," "expand," and "simplify." Factorizing is the process of finding factors that can divide a polynomial, while distributing is the opposite process, which involves multiplying terms by their coefficient. Expanding refers to multiplying brackets to produce an expression, while simplifying involves reducing an expression to its simplest form. Other synonyms may include "isolating," "separating," "extracting," and "dividing." Regardless of the synonym used, the central idea of factorization is to transform an expression into a more manageable form.