(x-3)(x+3)-(x+8)(x-8)

Jasonbradley

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Jun 17, 2024

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Simplifying the Expression: (x-3)(x+3) - (x+8)(x-8)

This article will guide you through simplifying the algebraic expression (x-3)(x+3) - (x+8)(x-8). We'll utilize the difference of squares pattern to achieve a concise solution.

Understanding the Difference of Squares

The difference of squares pattern states that: (a + b)(a - b) = a² - b². This pattern proves helpful in simplifying expressions containing two binomials with the same terms but differing signs.

Applying the Pattern

Let's apply this pattern to our expression:

1. (x-3)(x+3) follows the pattern where a = x and b = 3. Therefore, we can simplify it to x² - 3².

2. (x+8)(x-8) also follows the pattern where a = x and b = 8. Simplifying, we get x² - 8².

3. Now, our expression becomes: (x² - 3²) - (x² - 8²).

4. Expanding the brackets, we get: x² - 9 - x² + 64.

5. Combining like terms, we are left with: -9 + 64.

Final Result

Simplifying the expression (x-3)(x+3)-(x+8)(x-8) results in 55. The initial complex expression is reduced to a simple constant value, demonstrating the power of recognizing and applying algebraic patterns.