In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers.x² - 4

Verified step by step guidance

1. Identify the expression as a difference of squares: \(x^2 - 4\).
2. Recall the formula for factoring a difference of squares: \(a^2 - b^2 = (a - b)(a + b)\).
3. Recognize that \(x^2\) is a perfect square with \(a = x\) and \$4\( is a perfect square with \)b = 2$.
4. Apply the difference of squares formula: substitute \(a = x\) and \(b = 2\) into \((a - b)(a + b)\).
5. Write the factored form: \((x - 2)(x + 2)\).

Key Concepts

Difference of Squares

The difference of squares is a specific algebraic expression that takes the form a² - b², where a and b are any algebraic expressions. This expression can be factored into (a - b)(a + b). Understanding this concept is crucial for recognizing and applying the factoring technique to simplify expressions like x² - 4.

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In the case of the difference of squares, recognizing the structure allows for efficient simplification, which is a fundamental skill in algebra that aids in solving equations and simplifying expressions.

Exponents

Exponents represent the number of times a base is multiplied by itself. In the expression x² - 4, the exponent indicates that x is squared. Understanding exponents is essential for manipulating algebraic expressions, as they dictate the behavior of the variables involved, especially when factoring or simplifying expressions.