(x+3)(x+1)

Jasonbradley

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Jun 16, 2024

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Expanding (x+3)(x+1)

This article will walk you through the process of expanding the expression (x+3)(x+1). This is a common problem in algebra, and understanding the process is crucial for various mathematical applications.

Understanding the Concept

Expanding an expression like (x+3)(x+1) means multiplying the terms within the parentheses. This is achieved using the distributive property, which states that multiplying a sum by a number is equivalent to multiplying each term of the sum by the number.

Steps to Expand

1. Identify the terms: We have two terms, (x+3) and (x+1).
2. Distribute the first term: Multiply the first term, (x+3), by each term in the second parentheses, (x+1).
   • (x+3) * x = x² + 3x
   • (x+3) * 1 = x + 3
3. Combine the terms: Add the products obtained in step 2.
   • x² + 3x + x + 3
4. Simplify: Combine like terms.
   • x² + 4x + 3

Result

Therefore, the expanded form of (x+3)(x+1) is x² + 4x + 3.

Additional Notes

• Expanding expressions like this is essential for solving equations, simplifying expressions, and understanding graphs of quadratic functions.
• The FOIL method (First, Outer, Inner, Last) can be a helpful mnemonic for remembering the distribution process.
• Remember to combine like terms carefully to obtain the most simplified form of the expanded expression.