Question

Drag the correct values to the lines to create an expression equivalent to (2x - 5i) squared.

4x^2 + _____x+_________

-25i
-20i
-10i
10i
20i
25i
-25
-20
-10
10
20
25

Answer 1

To find an expression equivalent to \((2x - 5i)^2\), we can use the formula for the square of a binomial:

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

In this case, \(a = 2x\) and \(b = 5i\).

Now, we will calculate each part:

1. **Calculate \(a^2\)**:
\[
(2x)^2 = 4x^2
\]

2. **Calculate \(-2ab\)**:
\[
-2(2x)(5i) = -20xi
\]

3. **Calculate \(b^2\)**:
\[
(5i)^2 = 25i^2
\]
Since \(i^2 = -1\),
\[
25i^2 = 25(-1) = -25
\]

Combining these results, we have:
\[
(2x - 5i)^2 = 4x^2 - 20xi - 25
\]

Thus, placing the values in the form \(4x^2 + _____x + _______\), we get:

- The coefficient of \(x\) is \(-20\).
- The constant term is \(-25\).

So the completed expression is:
\[
4x^2 - 20x - 25
\]

To summarize, the values to fill in the blanks are:

- **For the first blank**: -20
- **For the second blank**: -25