(a+b)(a-2b)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (a+b)(a-2b)

This article explores the expansion of the expression (a+b)(a-2b) using the distributive property and provides a clear explanation of the process involved.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend separately by that number and then adding the products together. In simpler terms, it means we "distribute" the multiplication.

Expanding the Expression

1. Distribute the first term (a) from the first binomial:

   • a * (a-2b) = a² - 2ab

2. Distribute the second term (b) from the first binomial:

   • b * (a-2b) = ab - 2b²

3. Combine the results from steps 1 and 2:

   • (a² - 2ab) + (ab - 2b²)

4. Simplify by combining like terms:

   • a² - ab - 2b²

Final Result

Therefore, the expanded form of (a+b)(a-2b) is a² - ab - 2b².

Application of the Expanded Form

This expanded form has applications in various areas of mathematics, including:

• Algebraic manipulation: This expanded form can be used to simplify more complex expressions or solve equations.
• Factoring: Understanding the expansion of this expression can help with factoring quadratic expressions.
• Coordinate geometry: This expression can be used to represent lines and curves in coordinate geometry.

By understanding the distributive property and its application in expanding expressions like (a+b)(a-2b), we can effectively simplify and manipulate algebraic expressions in various contexts.