(a+5)(a-5)-3(a+2)(a-2)+5(a+4)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (a+5)(a-5)-3(a+2)(a-2)+5(a+4)

This article aims to simplify the given algebraic expression: (a+5)(a-5)-3(a+2)(a-2)+5(a+4). We will utilize the algebraic identities and the order of operations to achieve the simplest form.

Understanding the Identities

The given expression involves two important algebraic identities:

• Difference of Squares: (x + y)(x - y) = x² - y²
• Distributive Property: a(b + c) = ab + ac

Applying the Identities

Let's break down the simplification process step-by-step:

1. Applying the Difference of Squares:

   • (a+5)(a-5) = a² - 5² = a² - 25
   • 3(a+2)(a-2) = 3(a² - 2²) = 3(a² - 4) = 3a² - 12

2. Substituting the Simplified Terms:

   The original expression becomes: (a² - 25) - (3a² - 12) + 5(a + 4)

3. Applying the Distributive Property:

   • 5(a + 4) = 5a + 20

4. Combining like terms:

   The expression now is: a² - 25 - 3a² + 12 + 5a + 20

   Combining the terms: -2a² + 5a + 7

Conclusion

Therefore, the simplified form of the expression (a+5)(a-5)-3(a+2)(a-2)+5(a+4) is -2a² + 5a + 7.