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:
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Calculate \(a^2\): \[ (2x)^2 = 4x^2 \]
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Calculate \(-2ab\): \[ -2(2x)(5i) = -20xi \]
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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