In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. x²y² - 1

Key Concepts

Difference of Squares

The difference of squares is a specific algebraic expression that takes the form a² - b², which can be factored into (a - b)(a + b). This concept is fundamental in algebra as it simplifies expressions and solves equations efficiently. In the given expression x²y² - 1, it can be recognized as a difference of squares where a = xy and b = 1.

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. This is a crucial skill in algebra, as it allows for easier manipulation and solving of equations. In the context of the difference of squares, recognizing the structure of the expression enables the application of the factoring formula.

Variable Exponents

Variable exponents refer to the powers associated with variables in algebraic expressions. In the context of the problem, it is assumed that any variable exponents represent whole numbers, which simplifies the factoring process. Understanding how to handle variable exponents is essential for correctly applying algebraic rules and ensuring accurate factorization.