Algebraic identities are mathematical equations that hold true for all values of the variables involved. They express relationships between different algebraic expressions and are often used to simplify calculations or solve equations. Common examples include the difference of squares and perfect square trinomials. These identities are essential tools in algebra, allowing mathematicians and students to manipulate expressions efficiently. By recognizing and applying these identities, one can transform complex problems into simpler forms, making it easier to find solutions or prove other mathematical statements.