(a + b)(a - b)

Definition

(a + b)(a - b) is a special product in algebra that can be factored using the difference of two squares formula. This term represents the multiplication of two binomials, where one binomial is the sum of two variables and the other binomial is the difference of the same two variables.

5 Must Know Facts For Your Next Test

1. The expression $(a + b)(a - b)$ can be factored using the difference of two squares formula: $a^2 - b^2 = (a + b)(a - b)$.
2. Factoring $(a + b)(a - b)$ is a useful technique for simplifying algebraic expressions and solving equations.
3. The factors of $(a + b)(a - b)$ are $(a + b)$ and $(a - b)$, which are both binomials.
4. The product $(a + b)(a - b)$ is equal to $a^2 - b^2$, which is the difference of two squares.
5. Factoring $(a + b)(a - b)$ can be used to solve quadratic equations of the form $x^2 - k^2 = 0$, where $k$ is a constant.

Review Questions

• Explain the relationship between the expression $(a + b)(a - b)$ and the difference of two squares formula.
  • The expression $(a + b)(a - b)$ is directly related to the difference of two squares formula, $a^2 - b^2 = (a + b)(a - b)$. This formula can be used to factor the expression $(a + b)(a - b)$ by recognizing that it is the product of two binomials, where one is the sum of the variables $a$ and $b$, and the other is the difference of the same variables. Factoring $(a + b)(a - b)$ using the difference of two squares formula is a useful technique for simplifying algebraic expressions and solving equations.
• Describe how the factors of $(a + b)(a - b)$ can be used to solve quadratic equations of the form $x^2 - k^2 = 0$.
  • The factors of $(a + b)(a - b)$, which are $(a + b)$ and $(a - b)$, can be used to solve quadratic equations of the form $x^2 - k^2 = 0$, where $k$ is a constant. By recognizing that $x^2 - k^2 = (x + k)(x - k)$, the equation can be factored into the product of two binomials. This allows the equation to be solved by setting each factor equal to zero and solving for the values of $x$. The factorization of $(a + b)(a - b)$ using the difference of two squares formula is the key to solving these types of quadratic equations.
• Analyze the role of factoring $(a + b)(a - b)$ in simplifying algebraic expressions and solving equations.
  • Factoring the expression $(a + b)(a - b)$ is a crucial skill in simplifying algebraic expressions and solving equations. By recognizing that $(a + b)(a - b)$ can be factored using the difference of two squares formula, $a^2 - b^2 = (a + b)(a - b)$, the original expression can be broken down into a product of simpler binomial factors. This factorization process not only simplifies the expression but also provides a pathway to solving related equations. For example, factoring $(a + b)(a - b)$ can be used to solve quadratic equations of the form $x^2 - k^2 = 0$, where $k$ is a constant. The ability to factor $(a + b)(a - b)$ and apply the difference of two squares formula is a fundamental skill in intermediate algebra that enables students to manipulate and solve a wide range of algebraic problems.

Related terms

Binomial: A binomial is an algebraic expression with two terms, usually connected by addition or subtraction.

Difference of Two Squares: The difference of two squares is a special product formula that can be used to factor expressions of the form $a^2 - b^2$.

Factoring: Factoring is the process of breaking down a polynomial expression into a product of simpler expressions, such as binomials or monomials.