(a - b)(a + b)

Definition

(a - b)(a + b) is a special product in algebra, where the product of two binomials is simplified. It is a key concept in the context of 6.4 Special Products, which explores various methods for multiplying and factoring polynomial expressions.

5 Must Know Facts For Your Next Test

1. The expression (a - b)(a + b) can be simplified by using the difference of squares formula, where (a - b)(a + b) = a^2 - b^2.
2. This special product is commonly used in factoring polynomial expressions, as it allows for the factorization of a difference of squares.
3. The factors of (a - b)(a + b) are (a - b) and (a + b), which can be used to expand or simplify the expression.
4. The difference of squares formula is a useful tool for solving various algebraic problems, such as finding the area of a rectangle or simplifying complex expressions.
5. Understanding the properties of (a - b)(a + b) is crucial for mastering the concepts of 6.4 Special Products, as it lays the foundation for more advanced polynomial operations.

Review Questions

• Explain the difference of squares formula and how it relates to the expression (a - b)(a + b).
  • The difference of squares formula states that (a - b)(a + b) = a^2 - b^2. This formula is directly applicable to the expression (a - b)(a + b), as it allows you to simplify the product of the two binomials by subtracting the squares of the two terms. Understanding this relationship is crucial for factoring polynomial expressions and solving a variety of algebraic problems.
• Describe the process of factoring the expression (a - b)(a + b).
  • To factor the expression (a - b)(a + b), you can use the difference of squares formula. First, identify the two terms within the parentheses, a and b. Then, recognize that the expression can be written as a^2 - b^2. Finally, factor the expression by taking the square root of each term, resulting in the factors (a - b) and (a + b). This factorization process is an essential skill in 6.4 Special Products, as it allows you to simplify complex polynomial expressions.
• Analyze how the expression (a - b)(a + b) can be used to solve various algebraic problems.
  • The expression (a - b)(a + b) has numerous applications in algebra. For example, it can be used to find the area of a rectangle with dimensions (a - b) and (a + b), as the area would be (a - b)(a + b) = a^2 - b^2. Additionally, this expression can be used to simplify complex polynomial expressions, factor quadratic expressions, and solve various word problems involving differences of squares. Understanding the properties and applications of (a - b)(a + b) is crucial for success in 6.4 Special Products and beyond.

Related terms

Binomial:

A polynomial expression with two terms, typically in the form of a + b or a - b.

Difference of Squares:

A special product where one binomial is the difference of two squares, such as (a + b)(a - b).

Factoring:

The process of expressing a polynomial as a product of its factors.