Due: \( \frac{3-18-2025}{* *} \) This Factor the perfect square trinomial 1. \( x^{2}+18 x+81=1 \)

To factor the perfect square trinomial \( x^{2} + 18x + 81 \), we recognize that it follows the pattern \( (a + b)^{2} \). Here, \( a = x \) and \( b = 9 \), since \( 9 \times 9 = 81 \) and \( 2 \times 9 = 18 \). Therefore, we can write it as: \[ (x + 9)^2 = 1. \] Now, don't forget to consider the square root on both sides when solving for \( x \)! When you have \( (x + 9)^2 = 1 \), you can take the square root of both sides to find solutions: \( x + 9 = 1 \) or \( x + 9 = -1 \), leading you to \( x = -8 \) and \( x = -10 \). Solving it step by step is crucial to catching all the details!