(x+1)2-81

Jasonbradley

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Jun 16, 2024

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Factoring (x+1)² - 81

The expression (x+1)² - 81 can be factored using the difference of squares pattern. Here's how:

Difference of Squares

The difference of squares pattern states that:

a² - b² = (a + b)(a - b)

Applying the Pattern

1. Recognize the squares:

   • (x+1)² is the square of (x+1)
   • 81 is the square of 9

2. Substitute:

   • Let a = (x+1)
   • Let b = 9

3. Apply the pattern:

   • (x+1)² - 81 = (a + b)(a - b)
   • (x+1)² - 81 = (x+1 + 9)(x+1 - 9)

4. Simplify:

   • (x + 10)(x - 8)

Conclusion

Therefore, the factored form of (x+1)² - 81 is (x + 10)(x - 8).