(a+b+c)(a+b-c)-2ab

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (a+b+c)(a+b-c) - 2ab

This article explores the simplification of the algebraic expression (a+b+c)(a+b-c) - 2ab. We will use the distributive property and other algebraic techniques to arrive at a more concise form.

Applying the Distributive Property

The core of simplifying this expression lies in applying the distributive property. Let's break down the steps:

1. Expand the first product: (a+b+c)(a+b-c) can be expanded as follows:

   • a(a+b-c) + b(a+b-c) + c(a+b-c)

2. Distribute further:

   • a² + ab - ac + ab + b² - bc + ac + bc - c²

3. Combine like terms:

   • a² + 2ab + b² - c²

4. Subtract 2ab:

   • (a² + 2ab + b² - c²) - 2ab

5. Final simplification:

   • a² + b² - c²

Final Result

Therefore, the simplified form of the expression (a+b+c)(a+b-c) - 2ab is a² + b² - c².

This result demonstrates that complex-looking algebraic expressions can often be simplified through careful application of fundamental algebraic rules.