A² - b²

Definition

The expression a² - b² represents the difference between the squares of two numbers, a and b. This term is particularly important in the context of special products and factoring special products in algebra.

5 Must Know Facts For Your Next Test

1. The expression a² - b² can be factored as (a + b)(a - b), which is a common factoring technique.
2. The difference of squares formula is a useful tool for simplifying and expanding expressions involving a² - b².
3. The Binomial Theorem can be applied to the expression a² - b² to expand it into a more detailed form.
4. The term a² - b² is often encountered in problems involving special products and their factorization.
5. Understanding the properties and applications of a² - b² is crucial for success in algebra, particularly in the topics of special products and factoring.

Review Questions

• Explain how the expression a² - b² can be factored and the significance of this factorization.
  • The expression a² - b² can be factored as (a + b)(a - b). This factorization is significant because it allows you to rewrite the difference of two squares as the product of the sum and difference of the two numbers. This factorization technique is a key part of working with special products and is often used to simplify and manipulate algebraic expressions.
• Describe the relationship between the Binomial Theorem and the expression a² - b².
  • The Binomial Theorem provides a formula for expanding binomial expressions raised to a power. This theorem can be applied to the expression a² - b² to expand it into a more detailed form, such as (a + b)² - (a - b)². Understanding the Binomial Theorem and how it relates to a² - b² is important for working with special products and their expansions.
• Analyze the role of a² - b² in the context of special products and factoring special products.
  • The expression a² - b² is a key component of special products, such as the difference of squares. Recognizing and understanding a² - b² is crucial for successfully factoring these special products. By applying the difference of squares formula, you can factor a² - b² into the product of (a + b) and (a - b), which is a fundamental skill in algebra. The mastery of a² - b² and its applications is essential for navigating the topics of special products and their factorization.

Related terms

Perfect Square Difference: The difference between the squares of two numbers, where one number is the square root of the other.

Binomial Theorem: A formula that allows for the expansion of binomial expressions raised to a power.

Difference of Squares: A special product where the product of the sum and difference of two numbers is equal to the difference of their squares.