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\[
(x+9)^2 = x^2 + 18x + 81
\]
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To multiply \((x+9)^{2}\), you can use the formula \((a+b)^{2} = a^{2} + 2ab + b^{2}\). Here, \(a = x\) and \(b = 9\). So, we have: \[ (x+9)^{2} = x^{2} + 2 \cdot x \cdot 9 + 9^{2} = x^{2} + 18x + 81. \] Thus, \((x+9)^{2} = x^{2} + 18x + 81.\)