Multiply. \[ (x+9)^{2} \]

To expand \( (x+9)^{2} \), you can use the formula for squaring a binomial, which states that \( (a+b)^{2} = a^{2} + 2ab + b^{2} \). Here, \( a = x \) and \( b = 9 \). First, calculate \( a^{2} \): \( x^{2} \). Next, calculate \( 2ab \): \( 2 \cdot x \cdot 9 = 18x \). Finally, calculate \( b^{2} \): \( 9^{2} = 81 \). Putting it all together, you get: \[ (x+9)^{2} = x^{2} + 18x + 81. \]