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

Recognize the squares:
 (x+1)² is the square of (x+1)
 81 is the square of 9

Substitute:
 Let a = (x+1)
 Let b = 9

Apply the pattern:
 (x+1)²  81 = (a + b)(a  b)
 (x+1)²  81 = (x+1 + 9)(x+1  9)

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