In Exercises 39–48, factor the difference of two squares. 64x^2−81

The difference of squares is a specific algebraic identity that states that the difference between two squared terms can be factored into the product of their sum and difference. The general form is a^2 - b^2 = (a + b)(a - b). This concept is essential for simplifying expressions and solving equations involving squared terms.

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In the context of polynomials, factoring helps in simplifying expressions and solving equations. Understanding how to factor different types of polynomials, including the difference of squares, is a fundamental skill in algebra.

Quadratic expressions are polynomial expressions of degree two, typically in the form ax^2 + bx + c. In the case of the difference of squares, we specifically deal with expressions that can be rewritten as the difference between two squared terms. Recognizing and manipulating quadratic expressions is crucial for solving various algebraic problems, including factoring.