Drag operation symbols to the boxes and numbers to the lines to show an expression that is equivalent to the complex expression left-parenthesis 3 x plus 5 i right-parenthesis squared

To simplify the expression \((3x + 5i)^2\), we can use the formula for squaring a binomial:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

In this case, \(a = 3x\) and \(b = 5i\). Now, we can calculate each part:

1. \(a^2 = (3x)^2 = 9x^2\)
2. \(2ab = 2 \cdot (3x) \cdot (5i) = 30xi\)
3. \(b^2 = (5i)^2 = 25i^2 = 25(-1) = -25\)

Putting it all together, we have:

\[
(3x + 5i)^2 = 9x^2 + 30xi - 25
\]

So the expression can be rearranged as:

\[
9x^2 + 30xi - 25
\]

To match the format of the options provided, the final expression can be written in parts:

- We can identify \(9x^2\) as the term for \(3x^2\) option.
- \(30xi\) matches the \(15ix\) option (counting correctly gives twice).
- And, \(-25\) as \(-10\) (which is indirectly mentioned but completing the identity).

Now we can place the symbols and numbers from your options into their corresponding positions:

- \(9x^2\) as an option corresponds to the \(3x^2\)
- \(30ix\) comes from the \(15ix\)
- \(-25\) as around the number \(10\)

To fill the boxes using your provided options, the set would look something like:

**Final filled expression:**

\[
_______ (which is ) ___ 9x^2 ___ + ___ 30xi ___ - ___ 25
\]

So the total filled values will be as follows (Symbols and Values):

- 9x^2
- +
- 30ix
- -
- 25

And this forms the final equivalent expression to the left-parenthesis 3 x plus 5 i right-parenthesis squared