Expanding the Expression: (x+3)(x+2)
This article will delve into the process of expanding the algebraic expression (x+3)(x+2).
Understanding the Concept
The expression (x+3)(x+2) represents the product of two binomials. To expand it, we need to apply the distributive property. This property states that to multiply a sum by a number, we multiply each term of the sum by that number.
Expanding the Expression

Distribute the first term of the first binomial:
 Multiply (x) by each term in the second binomial:
 x * x = x²
 x * 2 = 2x
 Multiply (x) by each term in the second binomial:

Distribute the second term of the first binomial:
 Multiply (3) by each term in the second binomial:
 3 * x = 3x
 3 * 2 = 6
 Multiply (3) by each term in the second binomial:

Combine the terms:
 x² + 2x + 3x + 6

Simplify by combining like terms:
 x² + 5x + 6
The Final Result
Therefore, the expanded form of (x+3)(x+2) is x² + 5x + 6.
Applications of Expanding Binomials
Expanding binomials is a fundamental skill in algebra. It is essential for solving equations, simplifying expressions, and understanding various mathematical concepts. For instance:
 Factoring Quadratics: Understanding how to expand binomials is crucial when factoring quadratic expressions.
 Solving Equations: Expanding expressions allows us to solve equations by simplifying them into a solvable form.
 Graphing Functions: Expanding binomials can help us to determine the shape and location of graphs of quadratic functions.
Conclusion
Expanding binomials is a straightforward process that involves applying the distributive property. Understanding this process is crucial for mastering basic algebraic operations and solving more complex problems in mathematics.