(x+3)(x+2)

3 min read Jun 16, 2024

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