An algebraic identity is an equation that holds true for all values of the variables involved. It expresses a relationship between different algebraic expressions, showing that they are equivalent. For example, the identity a + b² = a² + 2ab + b² is true for any numbers a and b. These identities are useful in simplifying expressions and solving equations. They help in proving other mathematical statements and can be applied in various fields, including geometry and calculus. Understanding algebraic identities is fundamental for mastering higher-level mathematics.