(a + b)²

Definition

(a + b)² is a special product in algebra where the sum of two terms, a and b, is squared. This expression represents the result of multiplying the binomial (a + b) by itself, leading to a quadratic expression.

5 Must Know Facts For Your Next Test

1. The expanded form of (a + b)² is a² + 2ab + b².
2. The expression (a + b)² is a special case of the binomial theorem, which provides a formula for expanding any binomial raised to a power.
3. Factoring (a + b)² involves recognizing it as a perfect square, allowing the expression to be rewritten as (a + b)².
4. The expression (a + b)² is often used in simplifying algebraic expressions and solving equations.
5. Knowing the properties of (a + b)² is essential for factoring quadratic expressions and solving problems related to area and volume.

Review Questions

• Explain the process of expanding the expression (a + b)².
  • To expand the expression (a + b)², we use the formula for the square of a binomial: (a + b)² = a² + 2ab + b². This means that when we multiply the binomial (a + b) by itself, the result will be a quadratic expression with three terms: the square of the first term (a²), twice the product of the two terms (2ab), and the square of the second term (b²). Understanding this process is crucial for simplifying and manipulating algebraic expressions involving the square of a binomial.
• Describe the relationship between (a + b)² and the concept of a perfect square.
  • The expression (a + b)² is a perfect square because it represents the result of multiplying a binomial (a + b) by itself. A perfect square is the product of a number multiplied by itself, such as 4, 9, or 16. Recognizing (a + b)² as a perfect square allows us to factor the expression, which is an essential skill in solving quadratic equations and simplifying algebraic expressions. Understanding the connection between (a + b)² and perfect squares is crucial for applying various algebraic techniques in the context of 6.3 Factor Special Products.
• Explain how the properties of (a + b)² can be applied to solve problems related to area and volume.
  • The expression (a + b)² is closely related to the concept of area, as it represents the square of a binomial. For example, if we have a square with side lengths (a + b), the area of the square can be calculated using the formula (a + b)². Similarly, in problems involving the volume of a cube with side lengths (a + b), the volume can be expressed as (a + b)³, which is the cube of the binomial. Recognizing and applying the properties of (a + b)² is essential for solving problems that involve the relationships between algebraic expressions and geometric concepts, such as area and volume.

Related terms

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

Quadratic Expression: A quadratic expression is a polynomial expression of degree two, containing terms with variables raised to the power of two.

Perfect Square: A perfect square is the result of multiplying a number by itself, such as 4, 9, 16, etc.