To find an expression equivalent to \((x + 9i)^2\), we need to expand this expression using the formula for the square of a binomial, which is given by \((a + b)^2 = a^2 + 2ab + b^2\).
In this case, let \(a = x\) and \(b = 9i\). Applying the formula:
\[ (x + 9i)^2 = x^2 + 2(x)(9i) + (9i)^2 \]
Calculating each term:
- \(x^2\) remains \(x^2\).
- \(2(x)(9i) = 18xi\).
- \((9i)^2 = 81i^2\). Since \(i^2 = -1\), we have \(81i^2 = 81(-1) = -81\).
Now, combining all these results, we get:
\[ (x + 9i)^2 = x^2 + 18xi - 81 \]
Therefore, the equivalent expression is:
\[ \boxed{B. , x^2 + 18xi - 81} \]